tag:blogger.com,1999:blog-85952480771279866022024-03-06T14:12:55.288+08:00Sambimatika | Belajar Matematika SMP/MTsKumpulan materi, soal dan pembahasan matematika SMP/MTsNurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-8595248077127986602.post-8535873871217140332022-04-04T08:46:00.003+08:002022-10-27T21:42:08.528+08:00Pembahasan Soal Matematika Semester Genap Kelas 8<p><span style="font-size: medium;"> 1. Perhatikan gambar berikut !</span></p><p></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgySuCtdy2LmzXiKU7BzGP5kSCNDmGxy-UlObVFQUd6SYoJ8ZHNkBPPnlz1pckQQ4WGipD-MgFlmuXJRFYiLvDZkSVvMm83U_5mOPq0LIjaelg6Da1Se3kJibtUwWKsFVScGqB3OH8Z6N9dM1svrXBUCRxMXFB3WjNFje6Tx3cv4JBaqai26TmVN1vA" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="195" data-original-width="256" height="166" src="https://blogger.googleusercontent.com/img/a/AVvXsEgySuCtdy2LmzXiKU7BzGP5kSCNDmGxy-UlObVFQUd6SYoJ8ZHNkBPPnlz1pckQQ4WGipD-MgFlmuXJRFYiLvDZkSVvMm83U_5mOPq0LIjaelg6Da1Se3kJibtUwWKsFVScGqB3OH8Z6N9dM1svrXBUCRxMXFB3WjNFje6Tx3cv4JBaqai26TmVN1vA=w217-h166" title="Pembahasan Soal Semester Genap Kelas 8" width="217" /></span></a></p><p></p><p><span style="font-size: medium;">Nama daerah yang diarsir adalah</span></p><p><span style="font-size: medium;">A. Tembereng</span></p><p><span style="font-size: medium;">B. Juring</span></p><p><span style="font-size: medium;">C. Busur</span></p><p><span style="font-size: medium;">D. Tali busur</span></p><p><span style="font-size: medium;"><b>Kunci jawaban : A</b></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">2. Perhatikan gambar berikut !</span></p><p></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgSzU-lJ7ugViSRi9nh0de3wuFGP3aRcgzLCMkv8q9fhrOP790MJhYfv15YJLYg1RanRhUx6yxpsMBol5_Po1l7ydib-WHjklCmuF2HpE4YsonZsVaebT6-NbymA0oNlkYJIqkFmbsSdhn7rvuysOw6fEFDGKKwmW6KpktVLyH-s7BMAZFN70XZPuEe" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="227" data-original-width="272" height="191" src="https://blogger.googleusercontent.com/img/a/AVvXsEgSzU-lJ7ugViSRi9nh0de3wuFGP3aRcgzLCMkv8q9fhrOP790MJhYfv15YJLYg1RanRhUx6yxpsMBol5_Po1l7ydib-WHjklCmuF2HpE4YsonZsVaebT6-NbymA0oNlkYJIqkFmbsSdhn7rvuysOw6fEFDGKKwmW6KpktVLyH-s7BMAZFN70XZPuEe=w229-h191" title="Pembahasan Soal Semester Genap Kelas 8" width="229" /></span></a></p><p></p><p><span style="font-size: medium;">Jika <img src="https://latex.codecogs.com/svg.image?\angle&space;BOC=70^{o}" title="https://latex.codecogs.com/svg.image?\angle BOC=70^{o}" />, maka besar <img src="https://latex.codecogs.com/svg.image?\angle&space;OAB" title="https://latex.codecogs.com/svg.image?\angle OAB" /> adalah ....</span></p><p><span style="font-size: medium;">
A. <img src="https://latex.codecogs.com/svg.image?25^{o}" title="https://latex.codecogs.com/svg.image?25^{o}" /></span></p><p><span style="font-size: medium;">
B. <img src="https://latex.codecogs.com/svg.image?30^{o}" title="https://latex.codecogs.com/svg.image?30^{o}" /></span></p><p><span style="font-size: medium;">
C. <img src="https://latex.codecogs.com/svg.image?35^{o}" title="https://latex.codecogs.com/svg.image?35^{o}" /></span></p><p><span style="font-size: medium;">
D. <img src="https://latex.codecogs.com/svg.image?45^{o}" title="https://latex.codecogs.com/svg.image?45^{o}" /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><b>Pembahasan</b></span></p><p></p><blockquote><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BOC&space;" style="text-align: justify;" /><span style="text-align: justify;"> merupakan sudut pusat dan </span><img src="https://latex.codecogs.com/svg.image?\angle&space;OAB" style="text-align: justify;" /><span style="text-align: justify;"> merupakan sudut keliling. Hubungan antara sudut pusat dan sudut keliling yang menghadap busur yang sama adalah</span></span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\mathrm{Sudut\,&space;\,&space;Keliling}=\frac{1}{2}\mathrm{Sudut\,&space;\,&space;Pusat}" style="text-align: justify;" /></span></p><p></p></blockquote><p><span style="font-size: medium; text-align: justify;"><br /></span></p><p><span style="font-size: medium; text-align: justify;">Sehingga diperoleh</span></p><p><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;OAB=\frac{1}{2}\angle&space;BOC&space;" title="https://latex.codecogs.com/svg.image?\angle OAB=\frac{1}{2}\angle BOC" /></span></p><p>
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{1}{2}.70^{o}&space;" title="https://latex.codecogs.com/svg.image?=\frac{1}{2}.70^{o}" /></span></p><p>
<span style="font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=35^{o}" title="https://latex.codecogs.com/svg.image?=35^{o}" /></span></p><p><span style="font-size: medium;"><br /></span></p><p><span style="font-size: medium;">3. Perhatikan gambar berikut</span></p><p></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjcl4CdTMDQW8Qqo_ZbqOARPWq7geP69b0foc3hEZMBfSWqvZpXOUn_hwFKu5YO1NmECWkRxGEIIwtjFfK_LnqRUQ_7_KCUegmeq9Ky9KliJfLanI1E8SgkdhFoq7HpEIc9OMKRMTirU8iCZ3pEN7TsJJX_vWj34CE97Oz-Spc5tvr3ZhQFeHu_ARyi" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="207" data-original-width="230" height="164" src="https://blogger.googleusercontent.com/img/a/AVvXsEjcl4CdTMDQW8Qqo_ZbqOARPWq7geP69b0foc3hEZMBfSWqvZpXOUn_hwFKu5YO1NmECWkRxGEIIwtjFfK_LnqRUQ_7_KCUegmeq9Ky9KliJfLanI1E8SgkdhFoq7HpEIc9OMKRMTirU8iCZ3pEN7TsJJX_vWj34CE97Oz-Spc5tvr3ZhQFeHu_ARyi=w182-h164" title="Pembahasan Soal Semester Genap Kelas 8" width="182" /></span></a></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Titik O adalah pusat lingkaran. Jika diketahui <img src="https://latex.codecogs.com/svg.image?\angle&space;ABE+\angle&space;ACE+\angle&space;ADE=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ABE+\angle ACE+\angle ADE=96^{o}" />, maka besar
<img src="https://latex.codecogs.com/svg.image?\angle&space;AOE" title="https://latex.codecogs.com/svg.image?\angle AOE" /> adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. <img src="https://latex.codecogs.com/svg.image?32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?48^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?48^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?54^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?54^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?64^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?64^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ingat bahwa besarnya sudut keliling yang menghadap busur yang sama memiliki besar sama.</span></p><p style="text-align: justify;"><span style="font-size: medium;">Ambil <img src="https://latex.codecogs.com/svg.image?\angle&space;ACE" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ACE" /> dan misal <img src="https://latex.codecogs.com/svg.image?\angle&space;ACE=x" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ACE=x" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Karena <img src="https://latex.codecogs.com/svg.image?\angle&space;ABE=\angle&space;ACE=\angle&space;ADE" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ABE=\angle ACE=\angle ADE" />, maka</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;ABE+\angle&space;ACE+\angle&space;ADE=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle ABE+\angle ACE+\angle ADE=96^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?x+x+x=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x+x+x=96^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?3x=96^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?3x=96^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?x=\frac{96^{o}}{3}=32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x=\frac{96^{o}}{3}=32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?\angle&space;AOE=2\angle&space;ACE&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle AOE=2\angle ACE" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=2.32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=2.32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=64^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=64^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">4. Nilai <i>x</i> dari gambar dibawah adalah ....</span></p><p style="text-align: justify;"></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEixEzMWR_Gm0Um8aI74j-GZZCu8j31D6b-5nUnbCZaVX5U2q9r7f8xB8-vfsxAY5tKTkKF_ccpPZPuPnf4TeG0vSkhUe38Bby1El0qBqpKrckgyPhHkZlwlzXjFdrjI6bcttnGoaWWLNaCQk0vKLPWgynnJ-bIl0MFsJV-oQGKZr-drSbaWoASZp1kX" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="235" data-original-width="235" height="167" src="https://blogger.googleusercontent.com/img/a/AVvXsEixEzMWR_Gm0Um8aI74j-GZZCu8j31D6b-5nUnbCZaVX5U2q9r7f8xB8-vfsxAY5tKTkKF_ccpPZPuPnf4TeG0vSkhUe38Bby1El0qBqpKrckgyPhHkZlwlzXjFdrjI6bcttnGoaWWLNaCQk0vKLPWgynnJ-bIl0MFsJV-oQGKZr-drSbaWoASZp1kX=w167-h167" title="Pembahasan Soal Semester Genap Kelas 8" width="167" /></span></a></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">A. <img src="https://latex.codecogs.com/svg.image?32^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/svg.image?36^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?36^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/svg.image?42^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?42^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/svg.image?46^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?46^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ingat bahwa sudut keliling yang saling berhadapan dan kaki-kaki sudutnya berimpit memiliki jumlah besar sudut <img src="https://latex.codecogs.com/svg.image?180^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\angle&space;BAD+\angle&space;BCD=180^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle BAD+\angle BCD=180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?2x+3x=180^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?2x+3x=180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?5x=180^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?5x=180^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?x=36^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?x=36^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">5. Keliling lingkaran yang berdiameter 28 cm adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 88 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 77 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 66 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 67 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui d = 28 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?\pi&space;=\frac{22}{7}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\pi =\frac{22}{7}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ditanyakan K = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?K=\pi&space;d&space;=\frac{22}{7}.28=22.3=66&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?K=\pi d =\frac{22}{7}.28=22.3=66" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi keliling lingkaran adalah 66 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">6. Luas lingkaran dengan jari-jari 15 cm adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>A. 702,5 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>B. 705 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>C. 706,5 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>D. 700 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui : r = 15</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?\pi=3,14&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\pi=3,14" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>Ditanyakan : L = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?L=\pi&space;r^{2}=(3,14)(15)^{2}=3,14.225=706,5" style="text-align: left;" title="https://latex.codecogs.com/svg.image?L=\pi r^{2}=(3,14)(15)^{2}=3,14.225=706,5" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi luas lingkaran adalah 706,5 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">7. Perhatikan gambar berikut !</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgWlqkk7T6wAK0l9vBu9lMmFC_KpUL4-C5XF-z1k_HvzwiZVyOQIcRRuxjcgVWYeWcwKZdVg3lp0K6QVfO64jWWkSyGxpVmh4dboou-mG5zb3BAjcyThA8hi0howO3xBllVMzPjmcq_KsQT0sOYI3ek3J2aP6EDKKPLHzw6EWGtZywBcD8zyTH1JBYr" style="margin-left: 1em; margin-right: 1em;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="212" data-original-width="214" height="153" src="https://blogger.googleusercontent.com/img/a/AVvXsEgWlqkk7T6wAK0l9vBu9lMmFC_KpUL4-C5XF-z1k_HvzwiZVyOQIcRRuxjcgVWYeWcwKZdVg3lp0K6QVfO64jWWkSyGxpVmh4dboou-mG5zb3BAjcyThA8hi0howO3xBllVMzPjmcq_KsQT0sOYI3ek3J2aP6EDKKPLHzw6EWGtZywBcD8zyTH1JBYr=w154-h153" title="Pembahasan Soal Semester Genap Kelas 8" width="154" /></a></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Jika besar sudut </span><img src="https://latex.codecogs.com/svg.image?\angle&space;AOB=60^{o}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle AOB=60^{o}" /> dan OB = 20 cm, maka panjang busur AB adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 30 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B, 28 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 26,6 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 20,6 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui <img src="https://latex.codecogs.com/svg.image?\angle&space;AOB=\alpha&space;=60^{o}&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\angle AOB=\alpha =60^{o}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><i>OB</i> =<i> r</i> = 20 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"> <img src="https://latex.codecogs.com/svg.image?\pi=3,14&space;" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\pi=3,14" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ditanyakan : Panjang Busur AB = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\mathrm{Panjang\,&space;\,&space;Busur&space;\,&space;\,&space;AB}=\frac{\alpha&space;}{360}.\,&space;\mathrm{Luas\,&space;\,&space;lingkaran}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{Panjang\, \, Busur \, \, AB}=\frac{\alpha }{360}.\, \mathrm{Luas\, \, lingkaran}" /><span style="text-align: left;"> </span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> <span> </span></span></span><img src="https://latex.codecogs.com/svg.image?=\frac{\alpha&space;}{360^{o}}\pi&space;r^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{\alpha }{360^{o}}\pi r^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> <span> </span></span></span><img src="https://latex.codecogs.com/svg.image?=\frac{60^{o}&space;}{360^{o}}(3,14)&space;(20)^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{60^{o} }{360^{o}}(3,14) (20)^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> <span> </span></span></span><img src="https://latex.codecogs.com/svg.image?=\frac{1}{6}(3,14)&space;(400)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{1}{6}(3,14) (400)" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> <span> </span></span></span><img src="https://latex.codecogs.com/svg.image?=\frac{1}{6}(1.256)" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{1}{6}(1.256)" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> <span> </span></span></span><img src="https://latex.codecogs.com/svg.image?=209,33" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=209,33" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : Tidak ada yang benar</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">8. Perhatikan gambar berikut !</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhBjIDBW947mj4HdttbcFK31TX4-yxCk8nitQVHozuXIjwBSS8gg3Chg_ll0jL_0YGdaja01dDJcGbv_LyBoKlLdaTCxseXEd3HR-NhygvLvXMAQQ-d6KRrcu-BQJhL1GL-Cu5Kpm4cb_XV0Wjy-Qh5PCp_6tgi9yJDFLDvYXSc4CE7Q2_ryLzgDjc-" style="margin-left: 1em; margin-right: 1em;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="180" data-original-width="231" height="146" src="https://blogger.googleusercontent.com/img/a/AVvXsEhBjIDBW947mj4HdttbcFK31TX4-yxCk8nitQVHozuXIjwBSS8gg3Chg_ll0jL_0YGdaja01dDJcGbv_LyBoKlLdaTCxseXEd3HR-NhygvLvXMAQQ-d6KRrcu-BQJhL1GL-Cu5Kpm4cb_XV0Wjy-Qh5PCp_6tgi9yJDFLDvYXSc4CE7Q2_ryLzgDjc-=w187-h146" title="Pembahasan Soal Semester Genap Kelas 8" width="187" /></a></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Luas daerah yang diarsir adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>A. 224 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>B. 792 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>C. 812 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>D. 912 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Gambar diatas akan kita bagi menjadi empat persegi yang kongruen seperti pada gambar berikut :</span></p><p style="text-align: justify;"></p><p style="clear: both; text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiv7B_ORFr5byP2tQJ5LyKoLL19iqtVu2DsGN_ls7YvYRlXhnPjYIMkB-xs2WZMQiXWpaaqWBVnZ8JBMvoJEmQpsMLFpQAb0ECwp9AyUDZXxge4p7cUNl9h6BlmZ8VSddJ4TYnrWZ0uNfZ1AR4yiF5nFEcOWjHuXdArdwAWu-Jbiw1C_upCW6dRFeNX" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="231" data-original-width="299" height="193" src="https://blogger.googleusercontent.com/img/a/AVvXsEiv7B_ORFr5byP2tQJ5LyKoLL19iqtVu2DsGN_ls7YvYRlXhnPjYIMkB-xs2WZMQiXWpaaqWBVnZ8JBMvoJEmQpsMLFpQAb0ECwp9AyUDZXxge4p7cUNl9h6BlmZ8VSddJ4TYnrWZ0uNfZ1AR4yiF5nFEcOWjHuXdArdwAWu-Jbiw1C_upCW6dRFeNX=w250-h193" title="Pembahasan Soal Semester Genap Kelas 8" width="250" /></span></a></p></div><p></p><p style="text-align: left;"><span style="font-size: medium;">dimana <img src="https://latex.codecogs.com/svg.image?AOBS\cong&space;OCRB\cong&space;OCQD\cong&space;OAPD" title="https://latex.codecogs.com/svg.image?AOBS\cong OCRB\cong OCQD\cong OAPD" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Perhatikan persegi AOBS</span></p><p style="text-align: left;"><span style="font-size: medium;">Luas I = Luas daerah OBS yaitu Luas daerah yang tidak diarsir</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span>= Luas persegi AOBS - Luas 1/4 lingkaran SOA</span></p><p style="text-align: left;"><span style="font-size: medium;">Dari ini diketahui</span></p><p style="text-align: left;"><span style="font-size: medium;">AO = r = 20 cm</span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\pi=3,14&space;" title="https://latex.codecogs.com/svg.image?\pi=3,14" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\mathrm{Luas\,&space;\,&space;I}=&space;AO^{2}-\frac{1}{4}(3,14)(AO)^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{Luas\, \, I}= AO^{2}-\frac{1}{4}(3,14)(AO)^{2}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=&space;(20)^{2}-\frac{1}{4}(3,14)(20)^{2}" title="https://latex.codecogs.com/svg.image?= (20)^{2}-\frac{1}{4}(3,14)(20)^{2}" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=400-\frac{1}{4}(3,14)(400)" title="https://latex.codecogs.com/svg.image?=400-\frac{1}{4}(3,14)(400)" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=400-314" title="https://latex.codecogs.com/svg.image?=400-314" /></span></p><p style="text-align: left;">
<span style="font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=86" title="https://latex.codecogs.com/svg.image?=86" /></span></p><p style="text-align: left;"><span style="font-size: medium;">Karena Luas I = Luas II maka</span></p><p style="text-align: left;"><span style="font-size: medium;">Luas III = Luas persegi AOBS - (Luas I + Luas II)</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span>= 400 - (86 + 86)</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span>= 400 - 172</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span>= 228</span></p><p style="text-align: left;"><span style="font-size: medium;">Karena <img src="https://latex.codecogs.com/svg.image?AOBS\cong&space;OCRB\cong&space;OCQD\cong&space;OAPD" title="https://latex.codecogs.com/svg.image?AOBS\cong OCRB\cong OCQD\cong OAPD" /> maka :</span></p><p style="text-align: left;"><span style="font-size: medium;">Luas III = Luas IV = Luas V = Luas IV sehingga</span></p><p style="text-align: left;"><span style="font-size: medium;">Luas daerah yang diarsir = Luas III + Luas IV + Luas V + Luas 6</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span>= 4 x 228</span></p><p style="text-align: left;"><span style="font-size: medium;"><span> </span><span> </span><span> </span>= 912</span></p><p style="text-align: left;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">9. Dua lingkaran A dan B masing-masing berdiameter 36 cm dan 16 cm. Jika jarak titik pusat kedua lingkaran AB = 26 cm, panjang garis singgung persekutuan luar kedua lingkaran tersebut adalah ….</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 22 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 24 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 26 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 28 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Gambar dari kedua lingkaran pada soal diatas adalah</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="clear: both; text-align: center;"></p><p style="clear: both; text-align: center;"></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgcp8Ngi_Mtxw6t5-3zmw6omGHZtRzXNKWZGwNsSaDeJxKJyrDvs_j7ZZFIwau31E1fljFe519VicEo6dtaNpdG8xgtazuC9_eRG0g3Z7OQU4vzYx0PHfbklnOq3PRpU7p_v0aqOxLDqEtaUd_3Ch0ruImA7voITdzLlc5DesMLip8LUR3UI-bbNxwL" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="238" data-original-width="416" height="183" src="https://blogger.googleusercontent.com/img/a/AVvXsEgcp8Ngi_Mtxw6t5-3zmw6omGHZtRzXNKWZGwNsSaDeJxKJyrDvs_j7ZZFIwau31E1fljFe519VicEo6dtaNpdG8xgtazuC9_eRG0g3Z7OQU4vzYx0PHfbklnOq3PRpU7p_v0aqOxLDqEtaUd_3Ch0ruImA7voITdzLlc5DesMLip8LUR3UI-bbNxwL=w320-h183" title="Pembahasan Soal Semester Genap Kelas 8" width="320" /></span></a></p><p></p><p></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Berdasarkan soal diatas diketahui :</span></p><p style="text-align: justify;"><span style="font-size: medium;">rA = R = 18 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">rB = r = 8 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">AB = 26 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">ditanyakan : PQ = .....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?PQ=\sqrt{AB^{2}-(R-r)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?PQ=\sqrt{AB^{2}-(R-r)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{26^{2}-(18-8)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{26^{2}-(18-8)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{26^{2}-(10)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{26^{2}-(10)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> <span> </span></span><img src="https://latex.codecogs.com/svg.image?=\sqrt{(26+10)(26-10)}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{(26+10)(26-10)}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{(36)(16}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{(36)(16}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=6.4=24" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=6.4=24" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">
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<p style="text-align: justify;"><span style="font-size: medium;">10. Perhatikan gambar berikut !</span></p><p style="text-align: justify;"></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEitNtGE6sTeu83fUVtYhUX9rlK2jMD6o1EDvRxAfbyx2XNUr6hjPS7hut1U6M0Qb6JCBAmf-6wri_4Pkm9an-_yo9nxIUR8ZGB2UcxErYwmOUon9_g9aDRF92Y7wsw5b_3-JxXcMZkOL5ORMOK0Zhs0chORqlSGdc_sU7IJpI4wOXOBdBBjx20ODyMw" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="157" data-original-width="162" src="https://blogger.googleusercontent.com/img/a/AVvXsEitNtGE6sTeu83fUVtYhUX9rlK2jMD6o1EDvRxAfbyx2XNUr6hjPS7hut1U6M0Qb6JCBAmf-6wri_4Pkm9an-_yo9nxIUR8ZGB2UcxErYwmOUon9_g9aDRF92Y7wsw5b_3-JxXcMZkOL5ORMOK0Zhs0chORqlSGdc_sU7IJpI4wOXOBdBBjx20ODyMw=s16000" title="Pembahasan Soal Semester Genap Kelas 8" /></span></a></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Jika O adalah pusat lingkaran dengan keliling 220 cm. Luas daerah yang diarsir adalah ..... <img src="https://latex.codecogs.com/svg.image?\pi&space;=\frac{22}{7}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\pi =\frac{22}{7}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 3.850 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 1.925 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 962,5 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 880 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Diketahui : K = 220 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"> <img src="https://latex.codecogs.com/svg.image?\pi&space;=\frac{22}{7}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\pi =\frac{22}{7}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Ditanyakan : Luas daerah yang diarsir = ....?</span></p><p style="text-align: justify;"><span style="font-size: medium;">Langkah pertama mencari nilai r dari keliling yang diketahui</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?K=2\pi&space;r" style="text-align: left;" title="https://latex.codecogs.com/svg.image?K=2\pi r" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?220=2.\frac{22}{7}&space;r" style="text-align: left;" title="https://latex.codecogs.com/svg.image?220=2.\frac{22}{7} r" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?r=\frac{220.7}{22.2}=5.7=35" style="text-align: left;" title="https://latex.codecogs.com/svg.image?r=\frac{220.7}{22.2}=5.7=35" /></span></p><p style="text-align: justify;"></p><blockquote><span style="font-size: medium;"><br /><br /><br />Ingat kembali rumus hubungan luas juring, sudut pusat dan luas lingkaran yaitu<br /><br /></span><p style="text-align: center;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?\mathrm{Luas\,&space;\,&space;Juring}=\frac{\pi&space;}{360^{o}}\pi&space;r^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{Luas\, \, Juring}=\frac{\pi }{360^{o}}\pi r^{2}" /></span></p></blockquote><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Sehingga diperoleh :</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?L&space;=\frac{\alpha&space;}{360}\pi&space;r^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?L =\frac{\alpha }{360}\pi r^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{90&space;}{360}\pi&space;r^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{90 }{360}\pi r^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{90&space;}{360}.\frac{22}{7}&space;(35)^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{90 }{360}.\frac{22}{7} (35)^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{1&space;}{4}.22.5.35" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{1 }{4}.22.5.35" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><img src="https://latex.codecogs.com/svg.image?=\frac{1&space;}{4}.3850=962,5" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\frac{1 }{4}.3850=962,5" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>Jadi luas daerah yang diarsir adalah 962,5 </span><img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">11. Perhatikan gambar berikut!</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhvB2TWUQ4XnxTW9BBIzGXUc0Xz9FRCxiwfOb_ZL44KCay080YjAX1tdHPRkvlLmWUwgcoYPtvh_cEo-9cmErEAjb2yjjAkqXnukocZq6QKfA_8VHZFvdmy-qGaYTVnUKEuap13t56_2KnO-YnouGSGDXvjUv8c_N513-FX6EHMUgUMW9ISrOz8wBs_" style="margin-left: 1em; margin-right: 1em;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="153" data-original-width="340" height="96" src="https://blogger.googleusercontent.com/img/a/AVvXsEhvB2TWUQ4XnxTW9BBIzGXUc0Xz9FRCxiwfOb_ZL44KCay080YjAX1tdHPRkvlLmWUwgcoYPtvh_cEo-9cmErEAjb2yjjAkqXnukocZq6QKfA_8VHZFvdmy-qGaYTVnUKEuap13t56_2KnO-YnouGSGDXvjUv8c_N513-FX6EHMUgUMW9ISrOz8wBs_=w214-h96" title="Pembahasan Soal Semester Genap Kelas 8" width="214" /></a></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Jika panjang PQ = 17 cm, PM = 5 cm dan QN = 3 cm, maka panjang MN adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 9 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 12. cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 14 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 15 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?MN=\sqrt{PQ^{2}-(PM+QN)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?MN=\sqrt{PQ^{2}-(PM+QN)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{17^{2}-(5+3)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{17^{2}-(5+3)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{17^{2}-(8)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{17^{2}-(8)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{(17+8)(17-8)}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{(17+8)(17-8)}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=\sqrt{(25)(9)}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=\sqrt{(25)(9)}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/svg.image?=5.3=15" style="text-align: left;" title="https://latex.codecogs.com/svg.image?=5.3=15" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi panjang MN = 15 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">12. Panjang garis singgung persekutuan dalam dua lingkaran 8 cm. Jika jarak titik pusat kedua lingkaran 17 cm dan panjang jari-jari salah satu lingkaran 10 cm, maka panjang jari-jari lingkaran yang lain adalah ….</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 5 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 6 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 7 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 9 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Misal PGSD = panjang garis singung persekutuan dalam</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?r_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?r_{1}" /> = Jari-jari lingkaran 1</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?r_{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?r_{2}" /> = jari-jari lingkaran 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">d = jarak titik pusat kedua lingkaran</span></p><p style="text-align: justify;"><span style="font-size: medium;">Maka dari soal diketahui :</span></p><p style="text-align: justify;"><span style="font-size: medium;">PGSD = 8 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?r_{1}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?r_{1}" /> =10 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">d = 17 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">ditanyakan : <img src="https://latex.codecogs.com/svg.image?r_{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?r_{2}" /> = .....?</span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?PGSD=\sqrt{d^{2}-(r_{1}+r_{2})^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?PGSD=\sqrt{d^{2}-(r_{1}+r_{2})^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?8=\sqrt{17^{2}-(10+r_{2})^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8=\sqrt{17^{2}-(10+r_{2})^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?8^{2}={17^{2}-(10+r_{2})^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8^{2}={17^{2}-(10+r_{2})^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?8^{2}=17^{2}-(10+r_{2})^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8^{2}=17^{2}-(10+r_{2})^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?8^{2}-17^{2}=-(10+r_{2})^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8^{2}-17^{2}=-(10+r_{2})^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?(8+17)(8-17)=-(10+r_{2})^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?(8+17)(8-17)=-(10+r_{2})^{2}" /></span></p><div><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?(25)(-9)=-(10+r_{2})^{2}" title="https://latex.codecogs.com/svg.image?(25)(-9)=-(10+r_{2})^{2}" /></span></div><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?-225=-(10+r_{2})^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?-225=-(10+r_{2})^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?225=(10+r_{2})^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?225=(10+r_{2})^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?10+r_{2}=\sqrt{225}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?10+r_{2}=\sqrt{225}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?10+r_{2}=15" style="text-align: left;" title="https://latex.codecogs.com/svg.image?10+r_{2}=15" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?r_{2}=15-10=5" style="text-align: left;" title="https://latex.codecogs.com/svg.image?r_{2}=15-10=5" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi jari-jari lingkaran yang lain adalah 5 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">13. Diketahui dua buah lingkaran dengan pusat di A dan B, masing-masing berjari-jari 34 cm dan 10 cm. Garis CD merupakan garis singgung persekutuan luar. Bila garis CD = 32 cm, panjang AB adalah …</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 66 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 44 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 42 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 40 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?CD=\sqrt{AB^{2}-(R-r)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?CD=\sqrt{AB^{2}-(R-r)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?32=\sqrt{AB^{2}-(34-10)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32=\sqrt{AB^{2}-(34-10)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?32=\sqrt{AB^{2}-(24)^{2}}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32=\sqrt{AB^{2}-(24)^{2}}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?32^{2}=AB^{2}-(24)^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?32^{2}=AB^{2}-(24)^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?AB^{2}=32^{2}+(24)^{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AB^{2}=32^{2}+(24)^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?AB^{2}=1024+576" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AB^{2}=1024+576" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?AB^{2}=1600" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AB^{2}=1600" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/svg.image?AB=\sqrt{1600}=40" style="text-align: left;" title="https://latex.codecogs.com/svg.image?AB=\sqrt{1600}=40" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi jarak kedua titik pusat lingkaran adalah 40 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">14. Banyak diagonal sisi pada kubus adalah….</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 4</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 6</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 10</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 12</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Banyak diagonal sisi atau diagonal bidang kubus adalah 12</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">15. Sebuah balok dengan ukuran 10 cm x 8 cm x 5 cm ,Jumlah panjang rusuk balok tersebut adalah….</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 400 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 230 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 92 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 23 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Jumlah panjang rusuk balok = 4(p + l + t)</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 4(10 + 8 + 5)</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 4(23)</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 92</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi jumlah panjang rusuk kubus adalah 92 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">16. Perhatikan jaring-jaring kubus berikut!</span></p><p style="text-align: justify;"><span style="font-size: medium;"></span></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhC4i8WiBohm80pKWbhMHrAr-jztsMPD-fWcbhUd5FWxN6r76dBorosDhLVDcOfofpPB6i49N1L43MgT3sb0-NusGTn6cOZX2l--KhjpfwwS-mt4uPsTLQARBAfN9SMx9xOp2JEOMN8uKV2kumZAVNc50Mtl7UF2f0QniqxdDUuW5eoAQGQw0TzFeQc" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="151" data-original-width="213" src="https://blogger.googleusercontent.com/img/a/AVvXsEhC4i8WiBohm80pKWbhMHrAr-jztsMPD-fWcbhUd5FWxN6r76dBorosDhLVDcOfofpPB6i49N1L43MgT3sb0-NusGTn6cOZX2l--KhjpfwwS-mt4uPsTLQARBAfN9SMx9xOp2JEOMN8uKV2kumZAVNc50Mtl7UF2f0QniqxdDUuW5eoAQGQw0TzFeQc=s16000" title="Pembahasan Soal Semester Genap Kelas 8" /></span></a></p><p></p><p style="text-align: justify;"><span style="font-size: medium;">Jika persegi yang diarsir merupakan sisi atas (tutup) kubus, maka yang menjadi alas kubus tersebut adalah persegi nomor ...</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 2</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 4</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">17. Sebuah kubus dengan panjang rusuk 8 cm, panjang diagonal ruang kubus adalah ....</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 8,3 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span>B. </span><img src="https://latex.codecogs.com/svg.image?8\sqrt{3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8\sqrt{3}" /> cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"></span>C. 8,2 cm</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. <img src="https://latex.codecogs.com/svg.image?8\sqrt{2}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?8\sqrt{2}" /> cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Panjang diagonal ruang kubus = <img src="https://latex.codecogs.com/svg.image?a\sqrt{3}=8\sqrt{3}" style="text-align: left;" title="https://latex.codecogs.com/svg.image?a\sqrt{3}=8\sqrt{3}" /> cm</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : B</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;">18. Banyak bidang sisi limas segi empat adalah……</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 3</span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 4</span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 5</span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 6</span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Banyak sisi limas segi-n = n + 1</span></p><p style="text-align: justify;"><span style="font-size: medium;">Banyak sisi limas segi-4 = 4 +1 = 5</span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span>19. </span>Untuk mengemas tomat pada saat panen, Pak Anton akan membuat kotak berbentuk balok tanpa tutup dari triplek berukuran alas 1 m x 0,5 m dan tinggi 0,75 m. Luas triplek yang diperlukan adalah …</span></p><p style="text-align: justify;"><span style="font-size: medium;">A. 1,75 <img src="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">B. 2,25 <img src="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">C. 2,75 <img src="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;">D. 3,25 <img src="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">Luas permukaan balok tanpa tutup = 2(pt + lt) + pl</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 2[(1)(0,75)+(0,5)(0,75)] + (1)(0,5)</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 2(0,75+0,375) + 0,5</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 2(1,125)+0,5</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 2,25+0,5</span></p><p style="text-align: justify;"><span style="font-size: medium;">= 2,75</span></p><p style="text-align: justify;"><span style="font-size: medium;">Jadi luas permukaan balok tanpa tutup adalah 2,75 <img src="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{m}^{2}" /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : C</b></span></p><p style="text-align: justify;"><span style="font-size: medium;">
</span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">20. Prisma tegak yang mempunyai rusuk sebanyak 42 adalah …</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;">A. Prisma segi – 14</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;">B. Prisma segi – 21</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;">C. Prisma segi – 40</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;">D. Prisma segi – 42</span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;"><br /></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;"><b>Pembahasan</b></span></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="text-align: left;"><span style="font-size: medium;">Banyak rusuk prisma segi-n = 3n</span></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">42 = 3n</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">n = 14</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Jadi banyak rusuk prisma tegak segi-14 adalah 42</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><b>Kunci jawaban : A</b></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">21. Perhatikan gambar prisma dengan alas trapesium sama kaki berikut !</span></span></p><p style="text-align: left;"></p><p style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg7Gj-ucMxG2Jb8JmtxL8-L_gT-RqtsgkLZLVQCXxwqywQirZGufbYnoYfZrb37YQeyLQ74S4OCsxOJo79vs-2sebWOgQzuOfX2XLTqdM9xGJn-aHGJqtBJRqY8aHOam1sqa6j-vrkUZYIKUsgZOK0v1wolT_wxGV2qKVTXoxG7oO0_e-iy45uSTTpm" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="315" data-original-width="269" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg7Gj-ucMxG2Jb8JmtxL8-L_gT-RqtsgkLZLVQCXxwqywQirZGufbYnoYfZrb37YQeyLQ74S4OCsxOJo79vs-2sebWOgQzuOfX2XLTqdM9xGJn-aHGJqtBJRqY8aHOam1sqa6j-vrkUZYIKUsgZOK0v1wolT_wxGV2qKVTXoxG7oO0_e-iy45uSTTpm" title="Pembahasan Soal Semester Genap Kelas 8" width="205" /></span></a></span></p><p></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Jika panjang AB = 6 cm, BC = AD = 5 cm, CD = 14 cm, dan AE = 15 cm, maka luas permukaan prisma tersebut adalah ....</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">A. 450 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">B. 480 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">C. 500 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">D. 510 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><b>Pembahasan</b></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Perhatikan alas trapesium</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Akan dicari luas trapesium ABCD</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Perhatikan gambar berikut</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"></span></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhjoZC2kGhv-SF0lLZPpCtioRM_Daz8CyHAJG3iEoIGKgd1PtYiolUC7_77O9n1a8N_0HqDqEP6TKxQJxlX2eQTGLVvP9wytFUyAdWfBeEtLyh920ba6ySpXkF5-_z2hacOkMIO21mjYiwBLUWGhJ9Vf9Th5dUKq-MYdUlUE45GZB93q4P6c_Qowew7" style="margin-left: 1em; margin-right: 1em;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="213" data-original-width="279" height="176" src="https://blogger.googleusercontent.com/img/a/AVvXsEhjoZC2kGhv-SF0lLZPpCtioRM_Daz8CyHAJG3iEoIGKgd1PtYiolUC7_77O9n1a8N_0HqDqEP6TKxQJxlX2eQTGLVvP9wytFUyAdWfBeEtLyh920ba6ySpXkF5-_z2hacOkMIO21mjYiwBLUWGhJ9Vf9Th5dUKq-MYdUlUE45GZB93q4P6c_Qowew7=w230-h176" title="Pembahasan Soal Semester Genap Kelas 8" width="230" /></a></span></span></div><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Dengan menggunakan teorema pythagoras akan dicari panjang AP</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?AP=\sqrt{AD^{2}-DP^{2}}" title="https://latex.codecogs.com/svg.image?AP=\sqrt{AD^{2}-DP^{2}}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?AP=\sqrt{5^{2}-4^{2}}" title="https://latex.codecogs.com/svg.image?AP=\sqrt{5^{2}-4^{2}}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?AP=\sqrt{25-16}" title="https://latex.codecogs.com/svg.image?AP=\sqrt{25-16}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?AP=\sqrt{9}=3" title="https://latex.codecogs.com/svg.image?AP=\sqrt{9}=3" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Selanjutnya akan dicari luas trapesium ABCD</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?L=\frac{1}{2}AP(AB+CD)" title="https://latex.codecogs.com/svg.image?L=\frac{1}{2}AP(AB+CD)" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?L=\frac{1}{2}.3(6+14)" title="https://latex.codecogs.com/svg.image?L=\frac{1}{2}.3(6+14)" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;">
<span style="font-size: medium;"><img src="https://latex.codecogs.com/svg.image?L=\frac{1}{2}.3(20)=30" title="https://latex.codecogs.com/svg.image?L=\frac{1}{2}.3(20)=30" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Luas trapesium = luas alas = luas tutup</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Maka diperoleh :</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Luas alas prisma = 30 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Luas tutup prisma = 30 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Selanjutnya akan dicari luas sisi-sisi tegaknya</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">1. Luas ABFE = AB x AE = 6 x 15 = 90 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">2. Luas ADHE = AD x AE = 5 x 15 = 75 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">3. Luas BCGF = Luas ADHE = 75 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">4. Luas CDHG = CD x DH = 14 x 15 = 210 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Sehingga diperoleh</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">Luas Permukaan Prisma = Luas Alas + Luas Tutup + Luas ABFE + Luas ADHE + Luas BCGF + luas CDHG</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">= 30 + 30 + 90 + 75 + 75 + 210</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;">= 510 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{2}" /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><b>Kunci jawaban : D</b></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">22. Panjang rusuk kubus A = 4 cm dan panjang rusuk kubus B = 5 cm, perbandingan luas permukaa kubus A dan B adalah…</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">A. 13 : 19</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">B. 16 : 25</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">C. 15 : 23</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">D. 17 : 19</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><b>Pembahasan</b></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">Luas Kubus A : Luas Kubus B</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">4 x 4 x 4 : 4 x 5 x 5</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">16 : 25</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><b>Kunci jawaban : B</b></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">23. Volume balok berikut adalah ....</span></span></p><p style="text-align: justify;"></p><p style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhpxhqBUxv6PhTkRebzk5RN5ZTPwFkVAw_XrZkZFYKtQ2MmgmyAzPOirW37icCoKR1sIXhp9fLOpaxOKI0JAOd_pTmzO1NI7EfNy99Fqi3QjKY_MADG3U0u5fN7u8lEahqqJWYLlqgteP48-wTjGFnBlPGyXOVEw1y6qBAvRodZ-NgOFxQ4QLEx9WA3" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: medium;"><img alt="Pembahasan Soal Semester Genap Kelas 8" data-original-height="189" data-original-width="322" height="150" src="https://blogger.googleusercontent.com/img/a/AVvXsEhpxhqBUxv6PhTkRebzk5RN5ZTPwFkVAw_XrZkZFYKtQ2MmgmyAzPOirW37icCoKR1sIXhp9fLOpaxOKI0JAOd_pTmzO1NI7EfNy99Fqi3QjKY_MADG3U0u5fN7u8lEahqqJWYLlqgteP48-wTjGFnBlPGyXOVEw1y6qBAvRodZ-NgOFxQ4QLEx9WA3=w256-h150" title="Pembahasan Soal Semester Genap Kelas 8" width="256" /></span></a></span></p><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">A. 720 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">B. 670 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">C. 520 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">D. 470 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><br /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><b>Pembahasan</b></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">Diketahui</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">p = 15 cm</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">l = 8 cm</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">t = 6 cm</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">Ditanyakan : V = ....?</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">V = p x l x t</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><span> </span>= 15 x 8 x 6</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;"><span> </span>= 720</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-size: medium;">Jadi volume balok adalah 720 <img src="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" title="https://latex.codecogs.com/svg.image?\mathrm{cm}^{3}" /></span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><b>Kunci jawaban : A</b></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-size: medium;"><br /></span></p><p></p><p></p></span>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Kec. Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-80432958443916113472021-09-09T12:18:00.001+08:002021-09-09T12:18:37.997+08:00Kumpulan Soal UN SMP MTs<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana; font-size: medium;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHRrDYDUqVJORbxGSjBZiD_Wt9wY9VYneITAx0Nv46E8sE3g2wHKWqG2FAEsTMfBEDxUImIuKUcrm3BwI-z9Awc_GN_Eu0XYXsFPkL-pV6mRDhctUc_kaT-V2iaXYOEbKC07wMUe5MAok/s450/ujian-online.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="348" data-original-width="450" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHRrDYDUqVJORbxGSjBZiD_Wt9wY9VYneITAx0Nv46E8sE3g2wHKWqG2FAEsTMfBEDxUImIuKUcrm3BwI-z9Awc_GN_Eu0XYXsFPkL-pV6mRDhctUc_kaT-V2iaXYOEbKC07wMUe5MAok/w200-h154/ujian-online.png" width="200" /></a></span></div><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Ujian Nasional masih merupakan ujian yang menakutkan bagi sebagian siswa maupun guru atau sekolah. Sebenarnya ujian nasional tidak sesulit yang dibayangkan karena berdasarkan pengalaman beberapa tahun terakhir soal ujian nasional tingkat kesulitannya tidak terlalu tinggi, malahan lebih sulit soal ujian semester. Bagi bapak/ibu atau siswa-siswi yang ingin memiliki soal-soal ujian nasional matematika SMP/MTs Tahun Pelajaran 2012/2013, sebagai bahan persiapan Ujian Nasional Tahun Pelajaran 2013/2014 dapat di dowmload pada link berikut :</span></p><span style="font-family: verdana; font-size: medium;">1. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wQllYdzFsNmJxTTA/edit" target="_blank">Pembahasan Soal Matematika SMP/MTs</a><br />2. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wSU5xQ1BlTnhGUUU/edit" target="_blank">Soal Paket 1</a><br />3. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wcWxwY3VCSzFiZlE/edit" target="_blank">Soal Paket 2</a><br />4. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wbnZiMFE1by1QMXM/edit">Soal Paket 3</a><br />5. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wQncxbklUTnozOTQ/edit" target="_blank">Soal Paket 4</a><br />6. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wRy1RSWs5UlEtc3M/edit" target="_blank">Soal Paket 5</a><br />7. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wQlJ5YU1LdzJuY1U/edit" target="_blank">Soal Paket 6</a><br />8. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wU08yQkxwbFJwaUE/edit" target="_blank">Soal Paket 7</a><br />9. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wMG9nSTZraHFIVVk/edit" target="_blank">Soal Paket 8</a><br />10. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5weEhUaFVvUW0wZU0/edit" target="_blank">Soal Paket 9</a><br />11. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5weTQ0R0pvX2Z6bFU/edit" target="_blank">Soal Paket 10</a><br />12. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wTDNUVEltVWk0aXc/edit" target="_blank">Soal Paket 11</a><br />13. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wNnJpRkdRcUQwSWM/edit" target="_blank">Soal Paket 12</a><br />14. <a href="https://docs.google.com/file/d/0B6OTyF9qlf5wWEI2V21UTkdhZG8/edit" target="_blank">Soal Paket 13</a><br />15.<a href="https://docs.google.com/file/d/0B6OTyF9qlf5wanFOSzM2WHNCb00/edit" target="_blank"> Soal Paket 14</a><br /><br /><br /></span><div style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Semoga blog ini bermanfaat bagi kesuksesan Ujian Nasional Tahun Pelajaran 2013/2014. Amin. Kritik dan saran yang sifatnya membangun blog ini kami sangat harapkan.</span></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-66360512140286351322021-09-09T12:13:00.002+08:002021-09-09T12:13:47.180+08:00Pembahasan Soal Ulangan Harian Bilangan Berpangkat dan Bentuk Akar<p><span style="font-family: verdana; font-size: medium;"><b></b></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana; font-size: medium;"><b></b></span></div><span style="font-family: verdana; font-size: medium;"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggWZVXv1cPrxHnKrv0artwKyJqBM4tVtM1SyBbS4F7X30O_fYBKuK0MToEAd2PpgxJIbmao2NrMv_sXxzTxBlDNCxMz418CDqrfLALCX4yeoN8-mJZT04f3zpQBOQ3LbIsItPtKbSQlek/s500/Desain+tanpa+judul.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="500" height="20" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggWZVXv1cPrxHnKrv0artwKyJqBM4tVtM1SyBbS4F7X30O_fYBKuK0MToEAd2PpgxJIbmao2NrMv_sXxzTxBlDNCxMz418CDqrfLALCX4yeoN8-mJZT04f3zpQBOQ3LbIsItPtKbSQlek/w20-h20/Desain+tanpa+judul.png" stile="float:left; margin:5px 9px;" width="20" /></a>Soal 1</b> </span><p></p><p><span style="font-family: verdana; font-size: medium;">Tentukan hasil dari operasi perpangkatan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{64^{2}+16^{3}}{4^{5}}" title="\frac{64^{2}+16^{3}}{4^{5}}" /></p><p><span style="font-family: verdana; font-size: medium;"><br /></span></p><p><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{64^{2}+16^{3}}{4^{5}}=\frac{\left&space;(&space;4^{3}&space;\right&space;)^{2}+\left&space;(&space;4^{2}&space;\right&space;)^{3}}{4^{5}}" title="\frac{64^{2}+16^{3}}{4^{5}}=\frac{\left ( 4^{3} \right )^{2}+\left ( 4^{2} \right )^{3}}{4^{5}}" /></p><p>
<span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{4^{6}+4^{6}}{4^{5}}" title="=\frac{4^{6}+4^{6}}{4^{5}}" /></p><p>
<span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{2x4^{6}}{4^{5}}" title="=\frac{2x4^{6}}{4^{5}}" /></p><p>
<span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=2x4^{6-5}" title="=2x4^{6-5}" /></p><p>
<span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=2x4=8" title="=2x4=8" /></p><p><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 2</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dapatkan bentuk perpangkatan yang ekivalen dengan bilangan dibawah ini. (Jawaban dapat lebih dari satu bentuk perpangkatan)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt[2]{8}" title="\sqrt[2]{8}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt[3]{27}" title="\sqrt[3]{27}" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt[2]{8}=8^{\frac{1}{2}}" title="\sqrt[2]{8}=8^{\frac{1}{2}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;2^{3}&space;\right&space;)^{\frac{1}{2}}" title="=\left ( 2^{3} \right )^{\frac{1}{2}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=2^{\frac{3}{2}}" title="=2^{\frac{3}{2}}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt[3]{27}=27^{\frac{1}{3}}" title="\sqrt[3]{27}=27^{\frac{1}{3}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;3^{3}&space;\right&space;)^{\frac{1}{3}}" title="=\left ( 3^{3} \right )^{\frac{1}{3}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=3" title="=3" /></p><p style="text-align: justify;"><b><span style="font-family: verdana; font-size: medium;"><br /></span></b></p><p style="text-align: justify;"><b><span style="font-family: verdana; font-size: medium;">Soal 3</span></b></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Diketahui </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\left&space;(&space;x^{n-1}y^{n}&space;\right&space;)^{3}}{x^{2n}y^{6+n}}" title="\frac{\left ( x^{n-1}y^{n} \right )^{3}}{x^{2n}y^{6+n}}" /> <span style="font-family: verdana; font-size: medium;">senilai dengan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{a}y^{b}" title="x^{a}y^{b}" /><span style="font-family: verdana; font-size: medium;">. Tentukan nilai </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{b}{a}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{b}{a}" title="\frac{b}{a}" /></a></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Pembahasan</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\left&space;(&space;x^{n-1}y^{n}&space;\right&space;)^{3}}{x^{2n}y^{6+n}}=x^{a}y^{b}" title="\frac{\left ( x^{n-1}y^{n} \right )^{3}}{x^{2n}y^{6+n}}=x^{a}y^{b}" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\left&space;(&space;x^{n-1}&space;\right&space;)^{3}\left&space;(&space;y^{n}&space;\right&space;)^{3}}{x^{2n}y^{6+n}}=x^{a}y^{b}" title="\frac{\left ( x^{n-1} \right )^{3}\left ( y^{n} \right )^{3}}{x^{2n}y^{6+n}}=x^{a}y^{b}" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{x^{3n-3}y^{3n}}{x^{2n}y^{6+n}}=x^{a}y^{b}" title="\frac{x^{3n-3}y^{3n}}{x^{2n}y^{6+n}}=x^{a}y^{b}" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{3n-3}x^{-2n}y^{3n}y^{-(6+n)}=x^{a}y^{b}" title="x^{3n-3}x^{-2n}y^{3n}y^{-(6+n)}=x^{a}y^{b}" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{3n-2n-3}y^{3n-n-6}=x^{a}y^{b}" title="x^{3n-2n-3}y^{3n-n-6}=x^{a}y^{b}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{n-3}y^{2n-6}=x^{a}y^{b}" title="x^{n-3}y^{2n-6}=x^{a}y^{b}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dari kesamaan diatas terlihat bahwa</span></p>
<p style="text-align: left;"><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;n-3=a" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;n-3=a" title="n-3=a" /></a> <span style="font-family: verdana; font-size: medium;">dan</span>
<a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;2n-6=b" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2n-6=b" title="2n-6=b" /></a><span style="font-family: verdana; font-size: medium;">, maka</span></p><p style="text-align: left;"> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{b}{a}=\frac{2n-6}{n-3}=\frac{2(n-3)}{n-3}=2" title="\frac{b}{a}=\frac{2n-6}{n-3}=\frac{2(n-3)}{n-3}=2" /></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Soal 4</b></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Sederhanakan operasi perpangkatan berikut ini.</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y^{3}\left&space;(&space;3y&space;\right&space;)^{2}" title="y^{3}\left ( 3y \right )^{2}" /></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;">b. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{b}2y^{5}b^{3}6y^{2}" title="\sqrt{b}2y^{5}b^{3}6y^{2}" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;">c. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;m^{3}&space;\right&space;)^{4}4t^{3}" title="\left ( m^{3} \right )^{4}4t^{3}" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;">d. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;2x^{3}&space;\right&space;)3\left&space;(&space;x^{2}y^{2}&space;\right&space;)^{3}5y^{4}" title="\left ( 2x^{3} \right )3\left ( x^{2}y^{2} \right )^{3}5y^{4}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y^{3}\left&space;(&space;3y&space;\right&space;)^{2}=y^{3}3^{2}y^{2}" title="y^{3}\left ( 3y \right )^{2}=y^{3}3^{2}y^{2}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=9y^{3+2}" title="=9y^{3+2}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=9y^{5}" title="=9y^{5}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{b}2y^{5}b^{3}6y^{2}=2.6.b^{\frac{1}{2}}.b^{3}.y^{5}.y^{2}" title="\sqrt{b}2y^{5}b^{3}6y^{2}=2.6.b^{\frac{1}{2}}.b^{3}.y^{5}.y^{2}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=12b^{\frac{1}{2}+3}.y^{5+2}" title="=12b^{\frac{1}{2}+3}.y^{5+2}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=12b^{\frac{7}{2}}.y^{7}" title="=12b^{\frac{7}{2}}.y^{7}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">c. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;tn^{3}&space;\right&space;)^{4}4t^{3}=4t^{4}\left&space;(&space;n^{3}&space;\right&space;)^{4}t^{3}" title="\left ( tn^{3} \right )^{4}4t^{3}=4t^{4}\left ( n^{3} \right )^{4}t^{3}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4t^{4}n^{3.4}t^{3}" title="=4t^{4}n^{3.4}t^{3}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4t^{4}t^{3}n^{12}" title="=4t^{4}t^{3}n^{12}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4t^{4+3}n^{12}" title="=4t^{4+3}n^{12}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4t^{7}n^{12}" title="=4t^{7}n^{12}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">d. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;2x^{3}&space;\right&space;)3\left&space;(&space;x^{2}y^{2}&space;\right&space;)^{3}5y^{4}=2.3.5.x^{3}\left&space;(&space;x^{2}&space;\right&space;)^{3}\left&space;(&space;y^{2}&space;\right&space;)^{3}y^{4}" title="\left ( 2x^{3} \right )3\left ( x^{2}y^{2} \right )^{3}5y^{4}=2.3.5.x^{3}\left ( x^{2} \right )^{3}\left ( y^{2} \right )^{3}y^{4}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=30.x^{3}.x^{6}.y^{6}y^{4}" title="=30.x^{3}.x^{6}.y^{6}y^{4}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=30.x^{3+6}.y^{6+4}" title="=30.x^{3+6}.y^{6+4}" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=30x^{9}y^{10}" title="=30x^{9}y^{10}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Soal 5</b></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Tuliskan bilangan dibawah ini dalam notasi ilmiah</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. 0,00000056</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. 2.500.000</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">c. 0,98</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">d. 10.000.000.000.000</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. Langkah-langkah menuliskan notasi ilmiah bilangan dibawah 0.</span></p><p style="text-align: justify;"></p><ol><li><span style="font-family: verdana; font-size: medium;">Tulis angka bukan nol menjadi bilangan kurang dari 10 dari bilangan tersebut ----> 5,6</span></li><li><span style="font-family: verdana; font-size: medium;">Hitung berapa banyak semua angka nol sebelum angka di bilangan itu, ini akan menjadi pangkat negatif----> 7</span></li></ol><span style="font-family: verdana; font-size: medium;">Jadi</span><p></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;0,00000056=5,6x10^{-7}" title="0,00000056=5,6x10^{-7}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">b. Langkah-langkah menuliskan notasi ilmiah bilangan lebih dari 10</span></p><p style="text-align: justify;"></p><ol><li><span style="font-family: verdana; font-size: medium;">Tulis angka bukan nol dari bilangan tersebut menjadi bilangan kurang dari 10 ---->2,5</span></li><li><span style="font-family: verdana; font-size: medium;">Hitung banyak semua angka termasuk nol dari bilangan tersebut. Ini akan menjadi pangkat positif --->6</span></li></ol><span style="font-family: verdana; font-size: medium;">Jadi</span><p></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2.500.000=2,5x10^{6}" title="2.500.000=2,5x10^{6}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">c. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;0,98=9,8x10^{-1}" title="0,98=9,8x10^{-1}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">d. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;10.000.000.000.000=1x10^{13}=10^{13}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;10.000.000.000.000=1x10^{13}=10^{13}" title="10.000.000.000.000=1x10^{13}=10^{13}" /></a></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Selanjutnya untuk mempelajari cara menentukan akar persamaan kuadrat dengan cara melengkapkan kuadrat sempurna silahkan klik <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/menentukan-akar-persamaan-kuadrat-dengan-melengkapkan-kuadrat-sempurna%20.html">LINK INI.</a></span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-20142138887362538952021-09-09T12:10:00.002+08:002021-09-09T12:10:51.825+08:00Menentukan Akar Persamaan Kuadrat dengan Rumus ABC | Materi Matematika SMP/MTs Kelas 9<p style="text-align: justify;"></p><span style="font-family: verdana; font-size: medium;"><div style="text-align: justify;"><div style="text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMsAVAJV0I-x0NAmJAh7Lq5_tQaEeutHVakkUlzCvqC7t93habVxHMLNFAfF-KRFVVb1n_coCQYzUVYo-kXzDnv5LG4CDaJi2Jo415WM2qtnvz4anbANC_QT2jFtOzILbGQdd8RBP0VaE/s96/Desain+tanpa+judul.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="96" data-original-width="96" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMsAVAJV0I-x0NAmJAh7Lq5_tQaEeutHVakkUlzCvqC7t93habVxHMLNFAfF-KRFVVb1n_coCQYzUVYo-kXzDnv5LG4CDaJi2Jo415WM2qtnvz4anbANC_QT2jFtOzILbGQdd8RBP0VaE/s16000/Desain+tanpa+judul.png" stile="float:left; margin:5px 9px;" /></a></div><span style="font-family: verdana; font-size: medium;">Pada bagian sebelumnya kita sudah mempelajari bahwa persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" title="ax^{2}+bx+c=0" /><span style="font-family: verdana;"><span style="font-size: large;"> </span><span style="font-size: medium;">setara/senilai dengan</span><span style="font-size: medium;"> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=0" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=0" /> <span style="font-size: medium;"><span style="font-family: verdana;">yang dapat diselesaikan dengan membentuk kuadrat sempurna </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+p&space;\right&space;)^{2}+q=0" title="\left ( x+p \right )^{2}+q=0" /><span style="font-family: verdana;">dimana</span></span><span> <span style="font-family: verdana; font-size: medium;">nilai </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;p=\frac{b}{2a}" title="p=\frac{b}{2a}" /><span> <span style="font-family: verdana; font-size: medium;"> dan </span></span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;q=\frac{c}{a}-\left&space;(&space;\frac{b}{2a}&space;\right&space;)^{2}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q=\frac{c}{a}-\left&space;(&space;\frac{b}{2a}&space;\right&space;)^{2}" title="q=\frac{c}{a}-\left ( \frac{b}{2a} \right )^{2}" /></a><span style="font-family: verdana; font-size: medium;">sehingga diperoleh akar-akar persamaan kuadrat berikut.</span></div></span><p></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+p&space;\right&space;)^{2}+q=0" style="font-size: large;" title="\left ( x+p \right )^{2}+q=0" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+p&space;\right&space;)^{2}=-q" title="\left ( x+p \right )^{2}=-q" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{b}{2a}&space;\right&space;)^{2}=-\left&space;(&space;\frac{c}{a}-\left&space;(&space;\frac{b}{2a}&space;\right&space;)^{2}&space;\right&space;)" title="\left ( x+p \right )^{2}=-\left ( \frac{c}{a}-\left ( \frac{b}{2a} \right )^{2} \right )" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{b}{2a}&space;\right&space;)^{2}=\left&space;(\frac{b}{2a}&space;\right&space;)^{2}-\frac{c}{a}" title="\left ( x+\frac{b}{2a} \right )^{2}=\left (\frac{b}{2a} \right )^{2}-\frac{c}{a}" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x+\frac{b}{2a}=\pm&space;\sqrt{\left&space;(&space;\frac{b}{2a}\right&space;)^{2}-\frac{c}{a}}" title="x+\frac{b}{2a}=\pm \sqrt{\left ( \frac{b}{2a}\right )^{2}-\frac{c}{a}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}\pm&space;\sqrt{\left&space;(&space;\frac{b}{2a}\right&space;)^{2}-\frac{c}{a}}" title="x=-\frac{b}{2a}\pm \sqrt{\left ( \frac{b}{2a}\right )^{2}-\frac{c}{a}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}\pm&space;\sqrt{\frac{b^{2}}{4a^{2}}-\frac{c}{a}}" title="x=-\frac{b}{2a}\pm \sqrt{\frac{b^{2}}{4a^{2}}-\frac{c}{a}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}\pm&space;\sqrt{\frac{b^{2}}{4a^{2}}-\frac{4ac}{4a^{2}}}" title="x=-\frac{b}{2a}\pm \sqrt{\frac{b^{2}}{4a^{2}}-\frac{4ac}{4a^{2}}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}\pm&space;\sqrt{\frac{b^{2}-4ac}{4a^{2}}}" title="x=-\frac{b}{2a}\pm \sqrt{\frac{b^{2}-4ac}{4a^{2}}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}\pm&space;\frac{\sqrt{b^{2}-4ac}}{\sqrt{4a^{2}}}" title="x=-\frac{b}{2a}\pm \frac{\sqrt{b^{2}-4ac}}{\sqrt{4a^{2}}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jadi diperoleh akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" title="ax^{2}+bx+c=0" /> <span style="font-family: verdana; font-size: medium;">adalah</span></p><p style="text-align: center;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Rumus ini lebih dikenal dengan Rumus ABC</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nilai didalam akar dari rumus ABC diatas disebut sebagai diskriminan (D) yaitu :</span></p><p style="text-align: center;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;D=\sqrt{b^{2}-4ac}" title="D=\sqrt{b^{2}-4ac}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nilai diskriminan ini untuk menentukan jenis akar dari persamaan kuadrat yaitu :</span></p><p style="text-align: justify;"></p><ol><li><span style="font-family: verdana; font-size: medium;">Jika D>0, maka persamaan kuadrat memiliki akar-akar berbeda,</span></li><li><span style="font-family: verdana; font-size: medium;">Jika D=0, maka persamaan kuadrat memiliki akan-akar kembar,</span></li><li><span style="font-family: verdana; font-size: medium;">Jika D<0, maka persamaan kuadrat tidak memiliki akar real.</span></li></ol><span style="font-family: verdana; font-size: medium;"><div><span style="font-family: verdana; font-size: medium;"><br /></span></div><b>Contoh Soal 1</b></span><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan menggunakan rumus ABC, tentukan Jenis akar danakar-akarnya dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-5x-3=0" title="2x^{2}-5x-3=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dari persamaan kudrat diatas diketahui :</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><i>a = 2, b = -5</i> dan<i> c = -3</i>, maka :</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Untuk menentukan jenis akar, kita akan mencari nilai diskriminannya yaitu</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;D=b^{2}-4ac" title="D=b^{2}-4ac" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;-5&space;\right&space;)^{2}-4.2.\left&space;(&space;-3\right&space;)" title="=\left( -5 \right )^{2}-4.2.\left ( -3\right )" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=25+24=49" title="=25+24=49" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="font-family: verdana; font-size: medium;">Karena nilai diskriminan <i>D = 49, D>0</i> artinya bahwa persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-5x-3=0" style="font-family: "Times New Roman"; font-size: medium;" title="2x^{2}-5x-3=0" /><span style="font-family: verdana; font-size: large;"> </span><span style="font-family: verdana; font-size: medium;">memiliki akar real berbeda.</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Akar-akar dari persamaan kuadrat diatas adalah</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-\left&space;(&space;-5&space;\right&space;)\pm&space;\sqrt{\left&space;(&space;-5&space;\right&space;)^{2}-4.2.\left&space;(&space;-3&space;\right&space;)}}{2.2}" title="x_{1,2}=\frac{-\left ( -5 \right )\pm \sqrt{\left ( -5 \right )^{2}-4.2.\left ( -3 \right )}}{2.2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{5\pm&space;\sqrt{25+24}}{4}" title="x_{1,2}=\frac{5\pm \sqrt{25+24}}{4}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{5\pm&space;\sqrt{49}}{4}" title="x_{1,2}=\frac{5\pm \sqrt{49}}{4}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{5\pm&space;7}{4}" title="x_{1,2}=\frac{5\pm 7}{4}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=\frac{5+7}{4}=\frac{12}{4}=3" title="x_{1}=\frac{5+7}{4}=\frac{12}{4}=3" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}=\frac{5-7}{4}=\frac{-2}{4}=-\frac{1}{2}" title="x_{2}=\frac{5-7}{4}=\frac{-2}{4}=-\frac{1}{2}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-5x-3=0" title="2x^{2}-5x-3=0" /> <span style="font-family: verdana; font-size: medium;">adalah <i>x = 3</i> atau </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{1}{2}" title="x=-\frac{1}{2}" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Contoh Soal 2</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan menggunakan rumus ABC tentukan akar-akar dari persamaan kuadrat berikut.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x+6=0" title="x^{2}+5x+6=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>b. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-4=0" title="x^{2}-4=0" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>c. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9x^{2}-6x+1=0" title="9x^{2}-6x+1=0" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>d. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x+1=0" title="x^{2}+x+1=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x+6=0" title="x^{2}+5x+6=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Diketahui a = 1, b = 5 dan c = 6</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">maka</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p><p style="text-align: justify;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-5\pm&space;\sqrt{5^{2}-4.1.6}}{2.1}" title="=\frac{-5\pm \sqrt{5^{2}-4.1.6}}{2.1}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-5\pm&space;\sqrt{25-24}}{2}" title="=\frac{-5\pm \sqrt{25-24}}{2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-5\pm&space;1}{2}" title="=\frac{-5\pm 1}{2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=\frac{-5+1}{2}=\frac{-4}{2}=-2" title="x_{1}=\frac{-5+1}{2}=\frac{-4}{2}=-2" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}=\frac{-5-1}{2}=\frac{-6}{2}=-3" title="x_{2}=\frac{-5-1}{2}=\frac{-6}{2}=-3" /></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar-akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x+6=0" title="x^{2}+5x+6=0" /><span style="font-family: verdana;"> adalah x = -2 atau x = -3</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-4=0" style="font-family: verdana; font-size: large;" title="x^{2}-4=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Diketahui a = 1, b = 0 dan c = -4, maka</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p><p style="text-align: justify;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{0\pm&space;\sqrt{0^{2}-4.1.\left&space;(&space;-4&space;\right&space;)}}{2.1}" title="=\frac{0\pm \sqrt{0^{2}-4.1.\left ( -4 \right )}}{2.1}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{\pm&space;\sqrt{16}}{2}" title="=\frac{\pm \sqrt{16}}{2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{\pm&space;4}{2}" title="=\frac{\pm 4}{2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=\frac{4}{2}=2" title="x_{1}=\frac{4}{2}=2" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}=\frac{-4}{2}=-2" title="x_{2}=\frac{-4}{2}=-2" /></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-4=0" style="font-family: verdana;" title="x^{2}-4=0" /><span style="font-family: verdana;"> adalah x = 2 atau x = -2</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;"><br /></span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;">c. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9x^{2}-6x+1=0" style="font-family: verdana; font-size: large;" title="9x^{2}-6x+1=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Diketahui a = 9, b = -6 dan c = 1</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p><p style="text-align: justify;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;-6&space;\right&space;)\pm&space;\sqrt{\left&space;(&space;-6&space;\right&space;)^{2}-4.9.1}}{2.9}" title="=\frac{-\left ( -6 \right )\pm \sqrt{\left ( -6 \right )^{2}-4.9.1}}{2.9}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{6\pm&space;\sqrt{36-36}}{18}" title="=\frac{6\pm \sqrt{36-36}}{18}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{6}{18}=\frac{1}{3}" title="=\frac{6}{18}=\frac{1}{3}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9x^{2}-6x+1=0" style="font-family: verdana; font-size: large;" title="9x^{2}-6x+1=0" /><span style="font-family: verdana; font-size: medium;"> adalah akar kembar </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x=\frac{1}{3}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{1}{3}" title="x=\frac{1}{3}" /></a></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">d. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x+1=0" title="x^{2}+x+1=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Diketahui a = 1, b = 1, dan c = 1</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1,2}=\frac{-b\pm&space;\sqrt{b^{2}-4ac}}{2a}" title="x_{1,2}=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}" /></p>
<p style="text-align: left;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-1\pm&space;\sqrt{1^{2}-4.1.1}}{2.1}" title="=\frac{-1\pm \sqrt{1^{2}-4.1.1}}{2.1}" /></p><p style="text-align: left;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-1\pm&space;\sqrt{1-4}}{2}" title="=\frac{-1\pm \sqrt{1-4}}{2}" /></p><p style="text-align: left;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-1\pm&space;\sqrt{-3}}{2}" title="=\frac{-1\pm \sqrt{-3}}{2}" /></p><div><span style="font-size: medium;"><span style="font-family: verdana;">karena D < 0 yaitu D = -3 maka persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x+1=0" style="text-align: justify;" title="x^{2}+x+1=0" /><span style="font-family: verdana;"> tidak memiliki akar bilangan riil.</span></span></div><div><span style="font-size: medium;"><span style="font-family: verdana;"><br /></span></span></div><div><span style="font-size: medium;"><span style="font-family: verdana;">Selanjutnya untuk mempelajari menentukan akar persamaan kuadrat dengan cara memfaktorkan silahkan klik <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-materi-dan-soal-menentukan.html">LINK INI.</a></span></span></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-814881812909448412021-09-09T12:06:00.002+08:002021-09-09T12:06:39.405+08:00Jumlah dan Hasil Kali Akar Persamaan Kuadrat | Materi Matematika Kelas 9 SMP/MTs<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Pada penyelesaian persamaan kuadrat atau mencari akar persamaan kuadrat dengan tiga cara yaitu cara melengkapkan kuadrat sempurna, rumus ABC dan memfaktorkan harus menentukan suatu nilai p dan q sehingga memenuhi :</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=\left&space;(&space;x+p&space;\right&space;)\left&space;(&space;x+q&space;\right&space;)" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=\left ( x+p \right )\left ( x+q \right )" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+px+qx+pq" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+px+qx+pq" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+\left&space;(&space;p+q&space;\right&space;)x+pq" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+\left ( p+q \right )x+pq" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>Dengan cara ini kita dapatkan akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" title="ax^{2}+bx+c=0" /> <span>adalah </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x_{1}=-p" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-p" title="x_{1}=-p" /></a> <span>atau</span> <a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x_{2}=-q" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}=-q" title="x_{2}=-q" /></a></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Sehingga dari kesamaan diatas diperoleh :</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}+x_{2}=-p-q=-\left&space;(&space;p+q&space;\right&space;)=-\frac{b}{a}" title="x_{1}+x_{2}=-p-q=-\left ( p+q \right )=-\frac{b}{a}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}=\left&space;(&space;-p&space;\right&space;)\left&space;(&space;-q&space;\right&space;)=pq=\frac{c}{a}" title="x_{1}.x_{2}=\left ( -p \right )\left ( -q \right )=pq=\frac{c}{a}" /><span style="text-align: left;"> </span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Dari penjelasan diatas dapat disimpulkan bahwa :</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"><span>Jika </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}" title="x_{1}" /><span style="text-align: left;"><span> dan </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}" title="x_{2}" /><span style="text-align: left;"><span> adalah akar dari persamaan kuadrat </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" title="ax^{2}+bx+c=0" /> <span>maka :</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(1) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}+x_{2}=-\frac{b}{a}" title="x_{1}+x_{2}=-\frac{b}{a}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(2) </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}=\frac{c}{a}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}=\frac{c}{a}" title="x_{1}.x_{2}=\frac{c}{a}" /></a></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(3) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{2}+x_{2}^{2}=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)^{2}-2x_{1}x_{2}=\left&space;(&space;-\frac{b}{a}&space;\right&space;)^{2}-2\frac{c}{a}" title="x_{1}^{2}+x_{2}^{2}=\left ( x_{1}+x_{2} \right )^{2}-2x_{1}x_{2}=\left ( -\frac{b}{a} \right )^{2}-2\frac{c}{a}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(4) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{2}-x_{2}^{2}=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)^{2}-2x_{1}x_{2}=\left&space;(&space;-\frac{b}{a}&space;\right&space;)^{2}-2\frac{c}{a}" title="x_{1}^{2}-x_{2}^{2}=\left ( x_{1}+x_{2} \right )^{2}-2x_{1}x_{2}=\left ( -\frac{b}{a} \right )^{2}-2\frac{c}{a}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(5) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{3}+x_{2}^{3}=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)^{3}-3x_{1}x_{2}\left&space;(&space;x_{1}+x_{2}&space;\right&space;)=\left&space;(&space;\frac{-b}{a}&space;\right&space;)^{3}+\frac{3bc}{a^{2}}" title="x_{1}^{3}+x_{2}^{3}=\left ( x_{1}+x_{2} \right )^{3}-3x_{1}x_{2}\left ( x_{1}+x_{2} \right )=\left ( \frac{-b}{a} \right )^{3}+\frac{3bc}{a^{2}}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p>
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<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Contoh Soal 1</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span><span style="text-align: left;"><span>Jika </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}" title="x_{1}" /><span style="text-align: left;"><span> dan </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}" title="x_{2}" /><span style="text-align: left;"><span> adalah akar dari persamaan kuadrat </span></span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-4x-12=0" title="x^{2}-4x-12=0" /><span style="text-align: left;"><span>Hitunglah :</span></span><span> </span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(a) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}+x_{2}" title="x_{1}+x_{2}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span><span>(b) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}" title="x_{1}.x_{2}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span><span>(c) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{2}+x_{2}^{2}" title="x_{1}^{2}+x_{2}^{2}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span><span>(d) </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x_{1}^{3}+x_{2}^{3}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{3}+x_{2}^{3}" title="x_{1}^{3}+x_{2}^{3}" /></a></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>Dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-4x-12=0" title="x^{2}-4x-12=0" /><span> diketahui</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a = 1, b = -4 dan c = -12, maka</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">(a) <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}+x_{2}=-\frac{b}{a}=-\frac{\left&space;(&space;-4&space;\right&space;)}{1}=4" title="x_{1}+x_{2}=-\frac{b}{a}=-\frac{\left ( -4 \right )}{1}=4" /><span style="text-align: left;"> </span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">(b) <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}=\frac{c}{a}=\frac{\left&space;(&space;-12&space;\right&space;)}{1}=-12" title="x_{1}.x_{2}=\frac{c}{a}=\frac{\left ( -12 \right )}{1}=-12" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>(c) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{2}+x_{2}^{2}=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)^{2}-2x_{1}x_{2}=\left&space;(&space;-\frac{b}{a}&space;\right&space;)^{2}-2\frac{c}{a}" style="text-align: justify;" title="x_{1}^{2}+x_{2}^{2}=\left ( x_{1}+x_{2} \right )^{2}-2x_{1}x_{2}=\left ( -\frac{b}{a} \right )^{2}-2\frac{c}{a}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4^{2}-2\left&space;(&space;-12&space;\right&space;)" title="=4^{2}-2\left ( -12 \right )" /></span></p><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=16+24=40" title="=16+24=40" /></span></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>(d) </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{3}+x_{2}^{3}=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)^{3}-3x_{1}x_{2}\left&space;(&space;x_{1}+x_{2}&space;\right&space;)=\left&space;(&space;\frac{-b}{a}&space;\right&space;)^{3}+\frac{3bc}{a^{2}}" style="text-align: justify;" title="x_{1}^{3}+x_{2}^{3}=\left ( x_{1}+x_{2} \right )^{3}-3x_{1}x_{2}\left ( x_{1}+x_{2} \right )=\left ( \frac{-b}{a} \right )^{3}+\frac{3bc}{a^{2}}" /></span></p><div><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4^{3}-3\left&space;(&space;-12&space;\right&space;).4" title="=4^{3}-3\left ( -12 \right ).4" /></span></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=64+144=208" title="=64+144=208" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p>
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<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Contoh Soal 2</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span><span>Persamaan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}+qx+\left&space;(&space;q-1&space;\right&space;)=0" title="2x^{2}+qx+\left ( q-1 \right )=0" /><span> mempunyai akar-akar </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}" style="text-align: justify;" title="x_{1}" /> <span>dan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}" style="text-align: justify;" title="x_{2}" /><span>. Jika </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{2}+x_{2}^{2}=4" title="x_{1}^{2}+x_{2}^{2}=4" />, <span>tentukan nilai q!</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dari persamaan kuadrat diperoleh :</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a = 2, b = q dan c = q - 1</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Sehingga diperoleh</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}^{2}+x_{2}^{2}=4" title="x_{1}^{2}+x_{2}^{2}=4" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x_{1}+x_{2}&space;\right&space;)^{2}-2x_{1}x_{2}=4" title="\left ( x_{1}+x_{2} \right )^{2}-2x_{1}x_{2}=4" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-\frac{b}{a}&space;\right&space;)^{2}-2\frac{c}{a}=4" title="\left ( -\frac{b}{a} \right )^{2}-2\frac{c}{a}=4" /><span style="text-align: left;"> </span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-\frac{q}{2}&space;\right&space;)^{2}-2\left&space;(&space;\frac{q-1}{2}&space;\right&space;)=4" title="\left ( -\frac{q}{2} \right )^{2}-2\left ( \frac{q-1}{2} \right )=4" /></span></p>
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{q^{2}}{4}-q+1=4" title="\frac{q^{2}}{4}-q+1=4" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q^{2}-4q+4=16" title="q^{2}-4q+4=16" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q^{2}-4q-12=0" title="q^{2}-4q-12=0" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;q-6&space;\right&space;)\left&space;(&space;q+2&space;\right&space;)=0" title="\left ( q-6 \right )\left ( q+2 \right )=0" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;q-6&space;\right&space;)=0" title="\left ( q-6 \right )=0" /> atau <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;q+2&space;\right&space;)=0" title="\left ( q+2 \right )=0" /></span></p><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q=6" title="q=6" /><span> <span> </span><span> </span><span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q=-2" title="q=-2" /></span></div><div><span style="font-family: verdana; font-size: medium;"> </span></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-15981201312214525382021-09-09T12:04:00.002+08:002022-02-22T13:46:03.658+08:00Pembahasan Soal Cara Menyusun Persamaan Kuadrat Baru<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Untuk menyusun persamaan kuadrat baru kita akan menggunakan rumusan dari <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/hasil-jumlah-dan-hasil-kali-akar.html" target="_blank">jumlah dan hasil kali akar persamaan kuadrat</a> seperti yang telah dibahas pada postingan sebelum ini.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Langkah-langkah menentukan persamaan kuadrat baru :</span></p><p style="text-align: justify;"></p><ol><li><span style="font-family: verdana; font-size: medium;">Hitung Jumlah akar dari persamaan kuadrat awal </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}+x_{2}=-\frac{b}{a}" title="x_{1}+x_{2}=-\frac{b}{a}" /></li><li><span style="font-family: verdana; font-size: medium;">Hitung Hasil kali akar dari persamaan kuadrat awal </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}=\frac{c}{a}" title="x_{1}.x_{2}=\frac{c}{a}" /></li><li style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Lakukan penjumlahan akar dari persamaan kuadrat baru yang diketahui dan substitusi jumlah akar persamaan kuadrat awal</span></li><li style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Lakukan perkalian akar dari persamaan kuadrat baru yang diketahui dan subtitusi hasil kali akar persamaan kuadrat awal</span></li><li style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Langkah akhir substitusi nilai jumlah dan hasil kali akar baru dari langkah 3 dan 4 ke persamaan berikut </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;x_{1}+x_{2}&space;\right&space;)x+x_{1}.x_{2}=0" style="text-align: left;" title="x^{2}-\left ( x_{1}+x_{2} \right )x+x_{1}.x_{2}=0" /></li><li style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dari langkah 5 kita sudah mendapatkan persamaan kuadrat baru</span></li></ol><span style="font-family: verdana; font-size: medium;">
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b><br /></b></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Contoh Soal</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>Akar-akar persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-12x+2=0" title="3x^{2}-12x+2=0" /> adalah </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}" title="x_{1}" /><span style="font-family: verdana; font-size: medium;"> dan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}" title="x_{2}" /><span style="font-family: verdana; font-size: medium;">. Tentukan persamaan kuadrat baru yang akar-akarnya </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x_{1}&space;+2&space;\right&space;)" title="\left ( x_{1} +2 \right )" /><span style="font-family: verdana; font-size: large;"> </span><span style="font-family: verdana; font-size: medium;">dan</span><span style="font-family: verdana; font-size: large;"> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x_{2}&space;+2&space;\right&space;)" title="\left ( x_{2} +2 \right )" /><span style="font-family: verdana; font-size: large;">.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dari persamaan kuadrat awal diketahui a = 3, b = -12 dan c = 2</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. Hitung jumlah akar dari persamaan kuadrat awal</span></p><p style="text-align: justify;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}+x_{2}=-\frac{b}{a}=-\left&space;(&space;\frac{-12}{3}&space;\right&space;)=4" title="x_{1}+x_{2}=-\frac{b}{a}=-\left ( \frac{-12}{3} \right )=4" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. Hitung hasil kali akar persamaan kuadrat awal</span></p>
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}.x_{2}=\frac{c}{a}=\frac{2}{3}" title="x_{1}.x_{2}=\frac{c}{a}=\frac{2}{3}" /><div><span style="font-family: verdana; font-size: medium;">3. Lakukan penjumlahan akar persamaan kuadrat baru</span></div><div><span style="font-family: verdana; font-size: medium;"><br /></span></div>
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x_{1}+2&space;\right&space;)+\left&space;(&space;x_{2}+2&space;\right&space;)=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+2+2" title="\left ( x_{1}+2 \right )+\left ( x_{2}+2 \right )=\left ( x_{1}+x_{2} \right )+2+2" /> </span><div><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+4" title="=\left ( x_{1}+x_{2} \right )+4" /></span></div><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4+4" title="=4+4" /> <span style="color: red;">(Substitusi hasil dari langkah 1)</span></span></div><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=8" title="=8" /></span></div><p style="text-align: left;"></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>4. Lakukan perkalian akar persamaan kuadrat baru</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x_{1}+2&space;\right&space;)\left&space;(&space;x_{2}+2&space;\right&space;)=x_{1}.x_{2}+2x_{1}+2x_{2}+2.2" title="\left ( x_{1}+2 \right )\left ( x_{2}+2 \right )=x_{1}.x_{2}+2x_{1}+2x_{2}+2.2" /></span></p><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=x_{1}.x_{2}+2\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+4" title="=x_{1}.x_{2}+2\left ( x_{1}+x_{2} \right )+4" /><br /></span><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{2}{3}+2.4+4" title="=\frac{2}{3}+2.4+4" /> <span style="color: red;">(Substitusi hasil dari langkah 1 dan 2)</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{2}{3}+12" title="=\frac{2}{3}+12" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{38}{3}" title="=\frac{38}{3}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">5. Menyusun persamaan kuadrat baru</span></p><p style="text-align: left;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;x_{1}+x_{2}&space;\right&space;)x+x_{1}.x_{2}=0" title="x^{2}-\left ( x_{1}+x_{2} \right )x+x_{1}.x_{2}=0" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}" title="x^{2}" /> - </span><span style="font-size: medium;"><span style="font-family: verdana;">(Jumlah akar persamaan kuadrat baru)</span><span style="font-family: verdana;"><i>x +</i> </span><span style="font-family: verdana;">Hasil kali akar persamaan kuadrat baru = 0</span></span></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-8x+\frac{38}{3}=0" title="x^{2}-8x+\frac{38}{3}=0" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-24x+38=0" title="3x^{2}-24x+38=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p>
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<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bagi peserta didik yang senang dengan tantangan bisa melakukannya secara langsung tanpa melakukan langkah-langkah diatas.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Kita langsung memasukkan akar-akar persamaan kuadrat baru ke rumus umum </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;x_{1}+x_{2}&space;\right&space;)x+x_{1}.x_{2}=0" style="text-align: left;" title="x^{2}-\left ( x_{1}+x_{2} \right )x+x_{1}.x_{2}=0" /> <span style="font-family: verdana; font-size: medium;">yaitu :</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;((&space;x_{1}+2&space;\right&space;)+\left&space;(&space;x_{2}+2&space;\right&space;))x+\left&space;(&space;x_{1}+2&space;\right&space;)\left&space;(&space;x_{2}+2&space;\right&space;)=0" title="x^{2}-\left (( x_{1}+2 \right )+\left ( x_{2}+2 \right ))x+\left ( x_{1}+2 \right )\left ( x_{2}+2 \right )=0" /></p><p style="text-align: justify;"><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+4&space;\right&space;)x+x_{1}.x_{2}+2\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+4" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+4&space;\right&space;)x+x_{1}.x_{2}+2\left&space;(&space;x_{1}+x_{2}&space;\right&space;)+4=0" title="x^{2}-\left ( \left ( x_{1}+x_{2} \right )+4 \right )x+x_{1}.x_{2}+2\left ( x_{1}+x_{2} \right )+4=0" /></a></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;-\frac{b}{a}+4&space;\right&space;)x+\frac{c}{a}+2\left&space;(&space;-\frac{b}{a}&space;\right&space;)+4=0" title="x^{2}-\left ( -\frac{b}{a}+4 \right )x+\frac{c}{a}+2\left ( -\frac{b}{a} \right )+4=0" /></p>
<p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;-\left&space;(&space;\frac{-12}{3}&space;\right&space;)+4&space;\right&space;)x+\frac{2}{3}+2\left&space;(&space;-\left&space;(&space;\frac{-12}{3}&space;\right&space;)\right&space;)+4=0" title="x^{2}-\left ( -\left ( \frac{-12}{3} \right )+4 \right )x+\frac{2}{3}+2\left ( -\left ( \frac{-12}{3} \right )\right )+4=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-\left&space;(&space;4+4&space;\right&space;)x+\frac{2}{3}+2\left&space;(4\right&space;)+4=0" title="x^{2}-\left ( 4+4 \right )x+\frac{2}{3}+2\left (4\right )+4=0" /> </p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-8x+\frac{2}{3}+12=0" title="x^{2}-8x+\frac{2}{3}+12=0" /> </p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-8x+\frac{38}{3}=0" title="x^{2}-8x+\frac{38}{3}=0" /> <span style="color: red; font-family: verdana; font-size: medium;">(Sama-sama dikalikan 3)</span></p><div>
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-24x+38=0" title="3x^{2}-24x+38=0" /></div>
</span></span>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-90189704561994497102021-09-09T12:01:00.001+08:002022-02-22T13:41:06.172+08:00Fungsi Kuadrat dan Pembahasan Soal<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span></span></span></p><div style="text-align: left;"></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana; font-size: medium;"><span></span></span></div><span style="font-family: verdana; font-size: medium;"><div class="separator" style="clear: both; text-align: center;"></div><span><div style="text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnJC-uacaRjU8EjH570blM0lR1BVQ_qgRR9MC08fvCqkmJIJ-9gI00o62YN-HjVie26RdnXKc8vY_3n4tzbYq4O1HANbGWeJzE2GNx4ZtbJUGB0iUIOGReS8u7e9ESU_pDkLvqJMKKo6s/s848/football-field-image.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="450" data-original-width="848" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnJC-uacaRjU8EjH570blM0lR1BVQ_qgRR9MC08fvCqkmJIJ-9gI00o62YN-HjVie26RdnXKc8vY_3n4tzbYq4O1HANbGWeJzE2GNx4ZtbJUGB0iUIOGReS8u7e9ESU_pDkLvqJMKKo6s/w185-h106/football-field-image.jpg" stile="float:left; margin:5px 9px;" width="185" /></a></div>Fungsi kuadrat adalah fungsi f yang ditentukan oleh rumus </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=ax^{2}+bx+c" title="f(x)=ax^{2}+bx+c" /> <span>dengan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a,b,c\in&space;\mathbb{R}" title="a,b,c\in \mathbb{R}" /> dan <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a\neq&space;0" title="a\neq 0" />.</span><div><span style="font-family: verdana; font-size: medium;"><br /></span></div><div><span style="font-family: verdana; font-size: medium;"><br /></span><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Bentuk umum fungsi kuadrat</b></span></p><p style="text-align: center;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=ax^{2}+bx+c" title="f(x)=ax^{2}+bx+c" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Persamaan fungsi kuadrat</b></span></p><p style="text-align: center;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y=ax^{2}+bx+c" title="y=ax^{2}+bx+c" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Grafik fungsi kuadrat berbentuk parabola. Fungsi kuadrat memiliki ciri khas, yaitu pangkat tertinggi dari variabelnya adalah pangkat 2 atau berderajat 2.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Contoh fungsi kuadrat</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=x^{2}-3x-4" title="f(x)=x^{2}-3x-4" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">b. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=2x^{2}-8" title="f(x)=2x^{2}-8" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>c. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=-x^{2}+x" title="f(x)=-x^{2}+x" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bentuk grafik fungsi kuadrat berdasarkan nilai a, dan nilai diskriminan (D) sebagai berikut.</span></p><p style="text-align: justify;"></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0SE-X0QhRmZ7gtmdvysy8FtKMlhyphenhyphen7XN8kbjw_PDWEVRfQ49R4EZL4sFSRJASJ019n6u9zkAeQxYQTd8YDadKCAApVMRwUIW6NUtjBLD85bKsFar2SLy3yVaFnXU8IQS2yjjP5JguSVeg/s645/gambar+soal+52.PNG" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana; font-size: medium;"><img border="0" data-original-height="323" data-original-width="645" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0SE-X0QhRmZ7gtmdvysy8FtKMlhyphenhyphen7XN8kbjw_PDWEVRfQ49R4EZL4sFSRJASJ019n6u9zkAeQxYQTd8YDadKCAApVMRwUIW6NUtjBLD85bKsFar2SLy3yVaFnXU8IQS2yjjP5JguSVeg/w640-h320/gambar+soal+52.PNG" width="640" /></span></a></p><p style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW7GQ1z0CyRfKCqROaco0epn744s_sbBuaVQ7dtfvofXEBNOuL3WMA1f2Ho1ie3rNrk1rXOf6lb8YeihFYwvPTtby-jRUyPFydO2npkY7BFDdLJCWX_yFeewWfq9xV5zNkG4wGyExhKJA/s642/gambar+soal+53.PNG" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana; font-size: medium;"><img border="0" data-original-height="318" data-original-width="642" height="318" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW7GQ1z0CyRfKCqROaco0epn744s_sbBuaVQ7dtfvofXEBNOuL3WMA1f2Ho1ie3rNrk1rXOf6lb8YeihFYwvPTtby-jRUyPFydO2npkY7BFDdLJCWX_yFeewWfq9xV5zNkG4wGyExhKJA/w640-h318/gambar+soal+53.PNG" width="640" /></span></a></p><p style="clear: both; text-align: justify;"><b style="font-family: verdana; font-size: large;"><br /></b></p><p style="clear: both; text-align: justify;"><b style="font-family: verdana; font-size: large;">Istilah Pada Grafik Fungsi Kuadrat</b></p><span style="font-family: verdana; font-size: medium;"><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Pembuat Nol Fungsi</b></span></p><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;">Pembuat nol fungsi adalah suatu nilai x yang menjadikan f(x) atau y sama dengan nol. Untuk menyelesaikan ini bisa menggunakan cara pemfaktoran, melengkapi kuadrat sempurna atau rumus ABC.</span></p><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Sumbu Simetri</b></span></p><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;">Sumbu simetri adalah suatu garis yang membagi grafik fungsi kuadrat menjadi dua bagian yang sama.</span></p><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>Persamaan sumbu simetri dari </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=ax^{2}+bx+c" style="text-align: left;" title="f(x)=ax^{2}+bx+c" /><span style="text-align: left;"> </span><span style="text-align: left;">dengan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a,b,c\in&space;\mathbb{R}" style="text-align: left;" title="a,b,c\in \mathbb{R}" /><span style="text-align: left;"> dan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a\neq&space;0" style="text-align: left;" title="a\neq 0" /><span style="text-align: left;"> adalah</span></span></p><p style="clear: both; text-align: center;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}" title="x=-\frac{b}{2a}" /></span></p><p style="clear: both; text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Nilai balik fungsi</b></span></p><p style="clear: both; text-align: justify;"></p><span style="font-family: verdana; font-size: medium; text-align: justify;"><p></p><ul><li><span style="font-family: verdana; text-align: justify;"><span>Jika a < 0, maka nilai balik fungsi f merupakan nilai maksimum fungsi f yaitu </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y_{max}=f\left&space;(&space;\frac{-b}{2a}&space;\right&space;)=\frac{-D}{4a}" title="y_{max}=f\left ( \frac{-b}{2a} \right )=\frac{-D}{4a}" /> untuk <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}" style="text-align: center;" title="x=-\frac{b}{2a}" /> dan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;D=b^{2}-4ac" style="text-align: justify;" title="D=b^{2}-4ac" /></li></ul><p></p><p></p><ul><li><span style="font-family: verdana; text-align: justify;"><span>Jika a > 0, maka nilai balik fungsi f merupakan nilai minimum fungsi f yaitu </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y_{min}=f\left&space;(&space;\frac{-b}{2a}&space;\right&space;)=\frac{-D}{4a}" title="y_{min}=f\left ( \frac{-b}{2a} \right )=\frac{-D}{4a}" /> untuk <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{b}{2a}" style="text-align: center;" title="x=-\frac{b}{2a}" /> dan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;D=b^{2}-4ac" style="text-align: justify;" title="D=b^{2}-4ac" /></li></ul><p></p></span></span></div><div><span style="font-family: verdana; font-size: medium;"><br /></span></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Titik Balik</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>Titik balik adalah titik yang paling rendah atau titik yang paling tinggi yang dilalui oleh sumbu simetri grafik fungsi kuadrat. Koordinat titik balik dari fungsi kuadrat </span><span style="text-align: left;"> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=ax^{2}+bx+c" style="text-align: left;" title="f(x)=ax^{2}+bx+c" /><span style="text-align: left;"> </span><span style="text-align: left;">dengan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a,b,c\in&space;\mathbb{R}" style="text-align: left;" title="a,b,c\in \mathbb{R}" /><span style="text-align: left;"> dan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a\neq&space;0" style="text-align: left;" title="a\neq 0" /> <span>adalah</span></span></p><p style="text-align: center;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;\frac{-b}{2a},\frac{-D}{4a}&space;\right&space;)" title="\left ( \frac{-b}{2a},\frac{-D}{4a} \right )" /></span></p><p style="text-align: center;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><span style="font-family: verdana; font-size: medium;">
<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Contoh soal dan pembahasan</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span><span>1. Gambarlah grafik fungsi </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=x^{2}-2x+5" title="f(x)=x^{2}-2x+5" /> dengan domain </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;x|-4\leqslant&space;x\leq&space;2,x\in&space;\mathbb{R}&space;\right&space;\}" title="\left \{ x|-4\leqslant x\leq 2,x\in \mathbb{R} \right \}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Langkah-langkah menggambar</span></p><p style="text-align: justify;"></p><ul><li><span style="font-family: verdana; font-size: medium;">Koefesien dari <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}" title="x^{2}" /> sama dengan 1 maka grafik terbuka ke atas</span></li><li><span style="font-family: verdana; font-size: medium;">Cek nilai Diskriminan</span></li></ul><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;D=b^{2}-4ac" title="D=b^{2}-4ac" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;-2&space;\right&space;)^{2}-4.1.5" title="=\left ( -2 \right )^{2}-4.1.5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4-20" title="=4-20" /></span></p><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=-16" title="=-16" />
</span></div><div><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span>D < 0 artinya grafik berada diatas sumbu x</span></div><div><ul style="text-align: left;"><li><span style="font-family: verdana; font-size: medium;">Tentukan persamaan sumbu simetri</span></li></ul></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{-b}{2a}" title="x=\frac{-b}{2a}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;-2&space;\right&space;)}{2.1}" title="=\frac{-\left ( -2 \right )}{2.1}" /></span></p><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{2}{2}=1" title="=\frac{2}{2}=1" /></span></div><div><ul style="text-align: left;"><li><span style="font-family: verdana; font-size: medium;">Tentukan Nilai Balik minimumnya</span></li></ul></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y_{min}=\frac{-D}{4a}" title="y_{min}=\frac{-D}{4a}" /></span></p><p><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;-16&space;\right&space;)}{4.1}" title="=\frac{-\left ( -16 \right )}{4.1}" /></span></p><p><span style="font-family: verdana; font-size: medium;"></span></p><p><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{16}{4}=4" title="=\frac{16}{4}=4" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span></span><span style="font-family: verdana; font-size: medium;">Ja</span><span style="font-family: verdana; font-size: medium;">di titik balik minimumnya adalah (1,4)</span></p><div><ul style="text-align: left;"><li><span style="font-family: verdana; font-size: medium;">Titik potong terhadap sumbu y jika x = 0</span></li></ul></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y=x^{2}-2x+5" title="y=x^{2}-2x+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=0^{2}-2.0+5" title="=0^{2}-2.0+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=5" title="=5" /></span></p><div>
<span style="font-family: verdana; font-size: medium;"><span> </span><span> </span>Jadi titik potong terhadap sumbu y adalah <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;0,5&space;\right&space;)" title="\left ( 0,5 \right )" /></span></div><div><ul style="text-align: left;"><li><span style="font-family: verdana; font-size: medium;">Cari koordinat titik lain dari ujung domain fungsi</span></li></ul><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span>Untuk x = -4</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y=x^{2}-2x+5" title="y=x^{2}-2x+5" /></span></p></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;-4&space;\right&space;)^{2}-2\left&space;(&space;-4&space;\right&space;)+5" title="=\left ( -4 \right )^{2}-2\left ( -4 \right )+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=16+8+5" title="=16+8+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=29" title="=29" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> <span> </span></span>Koordinat titik <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-4,29&space;\right&space;)" title="\left ( -4,29 \right )" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> <span> </span></span>Untuk x = 2</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y=x^{2}-2x+5" title="y=x^{2}-2x+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=2^{2}-2.2+5" title="=2^{2}-2.2+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=4-4+5" title="=4-4+5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span><span> </span><span> </span> </span> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=5" title="=5" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> <span> </span></span>Koordinat titik <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;2,5&space;\right&space;)" title="\left ( 2,5 \right )" /></span></p><p style="text-align: left;"></p><ul style="text-align: left;"><li><span style="font-family: verdana; font-size: medium;">Gambar Grafik Fungsi</span></li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5u8xOUhJ1qzJF9BknAvf2nwzaxwOp54RHd12PPwm_E4f8fPYbt7jv9iTcJZkIXJU_kQX8FsqauUN6RDNV0_2aT2Cvk7muERueB785aPjLtFs1Fsnv81t3V6mNebfmtqljz-TckVNmWUY/s644/gambar+soal+54.png" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana; font-size: medium;"><img border="0" data-original-height="544" data-original-width="644" height="540" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5u8xOUhJ1qzJF9BknAvf2nwzaxwOp54RHd12PPwm_E4f8fPYbt7jv9iTcJZkIXJU_kQX8FsqauUN6RDNV0_2aT2Cvk7muERueB785aPjLtFs1Fsnv81t3V6mNebfmtqljz-TckVNmWUY/w640-h540/gambar+soal+54.png" width="640" /></span></a></div><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span><br /></span></span></p>
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<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>2. Jika </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=4a+ax-bx^{2}" title="f(x)=4a+ax-bx^{2}" />, dengan <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x\in&space;\mathbb{R},a,b\in" title="x\in \mathbb{R},a,b\in" /> bilangan bulat, <i>f(2) = -8</i> dan <i>f(-1) = -11</i></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. Tentukan nilai a dan b</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. tulislah fungsi f</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">c. Persamaan sumbu simetri f</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">d. Nilai balik f dan jenisnya</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">e. Koordinat titik balik f dan jenisnya.</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Pembahasan</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. Tentukan nilai a dan b</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(2)=-8" title="f(2)=-8" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;4a+2.a-b.2^{2}=-8" title="4a+2.a-b.2^{2}=-8" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;4a+2a-4b=-8" title="4a+2a-4b=-8" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;6a-4b=-8" title="6a-4b=-8" /><span> .......... Persamaan (1)</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(-1)=-11" title="f(-1)=-11" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;4a+a(-1)-b(-1)^{2}=-11" title="4a+a(-1)-b(-1)^{2}=-11" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;4a-a-b=-11" title="4a-a-b=-11" /></span></p><p style="text-align: left;">
<span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3a-b=-11" title="3a-b=-11" /> <span>................ Persamaan (2)</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span>Eliminasi b dari persamaan (1) dan (2)</span></p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlDzBBtINYHg0n-w8iZO3ahRE_iwMR6rqmajOq4eTFpWCetSVs_SQR_-NX30ZtHCXm8XsY871oh4o_ElGGNNqS-Ux9KaxYL4PvcrEQ_VHzbpW3Mn5HEPCv9R8jeU6dCortW76OugAxm1w/s348/gambar+soal+56.png" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana; font-size: medium;"><img border="0" data-original-height="149" data-original-width="348" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlDzBBtINYHg0n-w8iZO3ahRE_iwMR6rqmajOq4eTFpWCetSVs_SQR_-NX30ZtHCXm8XsY871oh4o_ElGGNNqS-Ux9KaxYL4PvcrEQ_VHzbpW3Mn5HEPCv9R8jeU6dCortW76OugAxm1w/s16000/gambar+soal+56.png" /></span></a></div><p></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span>Substitusi a = -6 ke persamaan (1)</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><i><span> </span>6a - 4b = -8</i></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><i><span> </span>6(-6) - 4b = -8</i></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><i><span> </span>-36 -4b = -8</i></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><i><span> </span>-4b = 28</i></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><i><span> </span>b = -7</i></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. Rumus fungsi kuadrat f adalah....</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=4a+ax-bx^{2}" title="f(x)=4a+ax-bx^{2}" /></span></p>
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=4\left&space;(&space;-6&space;\right&space;)+\left&space;(&space;-6&space;\right&space;)x-\left&space;(&space;-7&space;\right&space;)x^{2}" title="f(x)=4\left ( -6 \right )+\left ( -6 \right )x-\left ( -7 \right )x^{2}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=-24-6x+7x^{2}" title="f(x)=-24-6x+7x^{2}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;f(x)=7x^{2}-6x-24" title="f(x)=7x^{2}-6x-24" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">c. Persamaan sumbu simetri</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{-b}{2a}" title="x=\frac{-b}{2a}" /></span></p>
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{-\left&space;(-&space;6&space;\right&space;)}{2.7}" title="x=\frac{-\left (- 6 \right )}{2.7}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{6}{14}" title="x=\frac{6}{14}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{3}{7}" title="x=\frac{3}{7}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">d. Nilai bali fungsi f</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Karena nilai a>0 maka grafik fungsi f terbuka ke atas, maka fungsi f memiliki nilai minimal</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;y_{min}=\frac{-D}{4a}" title="y_{min}=\frac{-D}{4a}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;">
</span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;b^{2}-4ac&space;\right&space;)}{4a}" title="=\frac{-\left ( b^{2}-4ac \right )}{4a}" /></span></p>
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;\left&space;(&space;-6&space;\right&space;)^{2}-4.7.\left&space;(&space;-24&space;\right&space;)&space;\right&space;)}{4.7}" title="=\frac{-\left ( \left ( -6 \right )^{2}-4.7.\left ( -24 \right ) \right )}{4.7}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-(36+672)}{28}" title="=\frac{-(36+672)}{28}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-708}{28}" title="=\frac{-708}{28}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-117}{7}" title="=\frac{-117}{7}" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">e. Koordinat titik baliknya adalah </span><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;\frac{3}{7},\frac{-117}{7}&space;\right&space;)" title="\left ( \frac{3}{7},\frac{-117}{7} \right )" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><span style="font-family: verdana; font-size: medium;"><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI3aBf-1OwvLFSM5F9WLGQanv_EZbXPRGY93OtrpiPTeGZ2zFsi9aTi45Ncq75ysdkpHourF1Z4Sby-7wnP0MRMKyXsOzEPYDzcjR8spQ9_BgCMMf6dGTo65Xa8TfC_NGjzJh3DtUC_Ow/s459/gambar+soal+57.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="258" data-original-width="459" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI3aBf-1OwvLFSM5F9WLGQanv_EZbXPRGY93OtrpiPTeGZ2zFsi9aTi45Ncq75ysdkpHourF1Z4Sby-7wnP0MRMKyXsOzEPYDzcjR8spQ9_BgCMMf6dGTo65Xa8TfC_NGjzJh3DtUC_Ow/s320/gambar+soal+57.png" stile="float:left; margin:5px 9px;" width="320" /></a></span><span style="font-family: verdana; font-size: medium;"></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. Perhatikan gambar disamping. Persegi panjang ABCD dengan panjang 16 cm dan lebar 12 cm. Titik-titik E, F, G dan H berturut-turut terletak pada AB, BC, CD dan AD sehingga DG = CF = BE = AH = x cm. Tentukanlah luas minimum segi empat EFGH.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dari gambar terlihat bahwa :</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Luas segitiga EAH = Luas segitiga FCG</span></p><p><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{\Delta&space;EAH}=\frac{1}{2}AE.AH" title="L_{\Delta EAH}=\frac{1}{2}AE.AH" /></p><p><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{\Delta&space;EAH}=\frac{1}{2}\left&space;(&space;16-x&space;\right&space;)x" title="L_{\Delta EAH}=\frac{1}{2}\left ( 16-x \right )x" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"></span></p><p><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{\Delta&space;EAH}=\frac{1}{2}\left&space;(&space;16x-x^{2}&space;\right&space;)" title="L_{\Delta EAH}=\frac{1}{2}\left ( 16x-x^{2} \right )" /></p><div><br /></div><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Luas segitiga EBF = Luas segitiga GDH </span></p><p></p><div class="separator" style="clear: both; text-align: center;"></div><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{\Delta&space;EBF}=\frac{1}{2}EB.BF" title="L_{\Delta EBF}=\frac{1}{2}EB.BF" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{\Delta&space;EBF}=\frac{1}{2}x\left&space;(&space;12-x&space;\right&space;)" title="L_{\Delta EBF}=\frac{1}{2}x\left ( 12-x \right )" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{\Delta&space;EBF}=\frac{1}{2}\left&space;(&space;12x-x^{2}&space;\right&space;)" title="L_{\Delta EBF}=\frac{1}{2}\left ( 12x-x^{2} \right )" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Luas segi empat EFGH = L ABCD - </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(L_{\Delta&space;EBF}+L_{\Delta&space;GDH}+L_{\Delta&space;EAH}+L_{\Delta&space;FCG}&space;\right&space;)" title="\left (L_{\Delta EBF}+L_{\Delta GDH}+L_{\Delta EAH}+L_{\Delta FCG} \right )" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L=16.12-\left&space;(&space;\frac{1}{2}\left&space;(&space;12x-x^{2}&space;\right&space;)+\frac{1}{2}\left&space;(&space;12x-x^{2}&space;\right&space;)+\frac{1}{2}\left&space;(&space;16x-x^{2}&space;\right&space;)+\frac{1}{2}\left&space;(&space;16x-x^{2}&space;\right&space;)&space;\right&space;)" title="L=16.12-\left ( \frac{1}{2}\left ( 12x-x^{2} \right )+\frac{1}{2}\left ( 12x-x^{2} \right )+\frac{1}{2}\left ( 16x-x^{2} \right )+\frac{1}{2}\left ( 16x-x^{2} \right ) \right )" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=192-\left&space;(&space;\left&space;(&space;12x-x^{2}&space;\right&space;)+\left&space;(&space;16x-x^{2}&space;\right&space;)&space;\right&space;)" title="=192-\left ( \left ( 12x-x^{2} \right )+\left ( 16x-x^{2} \right ) \right )" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=192-\left&space;(&space;28x-2x^{2}&space;\right&space;)" title="=192-\left ( 28x-2x^{2} \right )" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=192-28x+2x^{2}" title="=192-28x+2x^{2}" /></p>
<p style="text-align: left;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=2x^{2}-28x+192" title="=2x^{2}-28x+192" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Kita dapatkan bahwa L merupakan fungsi kuadrat dan dapat ditulis menjadi :</span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L(x)=2x^{2}-28x+192" title="L(x)=2x^{2}-28x+192" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Karena a = 2 > 0, maka nilai L adalah minimum, yaitu :</span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;L_{min}=\frac{-D}{4a}" title="L_{min}=\frac{-D}{4a}" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;b^{2}-4ac&space;\right&space;)}{4a}" title="=\frac{-\left ( b^{2}-4ac \right )}{4a}" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;\left&space;(&space;-28&space;\right&space;)^{2}-4.2.192&space;\right&space;)}{4.2}" title="=\frac{-\left ( \left ( -28 \right )^{2}-4.2.192 \right )}{4.2}" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{-\left&space;(&space;784-1536&space;\right&space;)}{8}" title="=\frac{-\left ( 784-1536 \right )}{8}" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{752}{8}" title="=\frac{752}{8}" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=94" title="=94" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Jadi luas minimum segi empat EFGH adalah 94 </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;cm^{2}" title="cm^{2}" />.</p></span></span></span>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0Aikmel Bar., Aikmel, Kabupaten Lombok Timur, Nusa Tenggara Bar., Indonesia-8.5728618 116.5182208-36.883095636178844 81.3619708 19.737372036178847 151.6744708tag:blogger.com,1999:blog-8595248077127986602.post-81160553002201438652021-08-09T18:17:00.118+08:002022-02-22T13:44:19.099+08:00Pembahasan Materi dan Soal Menentukan Akar Persamaan Kuadrat Dengan Pemfaktoran | Matematika SMP/MTs kelas 9<p><b><span style="font-family: verdana; font-size: medium;">Memfaktorkan bentuk persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0,a=1" title="ax^{2}+bx+c=0,a=1" /></b></p><p><span style="font-family: verdana; font-size: medium;">Tahap inti dari cara ini adalah memfaktorkan bentuk menjadi </span><span style="font-family: verdana; font-size: medium;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+bx+c=0" title="x^{2}+bx+c=0" />menjadi</span> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+p&space;\right&space;)\left&space;(&space;x+q&space;\right&space;)" title="\left ( x+p \right )\left ( x+q \right )" /> <span style="font-family: verdana; font-size: medium;">yang dapat dituliskan menjadi :</span></p><p style="text-align: center;"> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+bx+c=\left&space;(&space;x+p&space;\right&space;)\left&space;(&space;x+q&space;\right&space;)" title="x^{2}+bx+c=\left ( x+p \right )\left ( x+q \right )" /></p><p style="text-align: center;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+bx+c=x^{2}+\left&space;(&space;p+q&space;\right&space;)x+\left&space;(&space;p.q&space;\right&space;)" title="x^{2}+bx+c=x^{2}+\left ( p+q \right )x+\left ( p.q \right )" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Artinya untuk memfaktorkan bentuk ini harus mencari bilangan <i>p</i> dan <i>q</i> sedemikian hingga <i>b = p+q</i> dan <i>c = p.q</i></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Contoh 1</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan cara memfaktorkan, tentukan akar dari persamaan kuadrat berikut</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+6x+8=0" title="x^{2}+6x+8=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-7x+10=0" title="x^{2}-7x+10=0" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">c. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+2x-15=0" title="x^{2}+2x-15=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+6x+8=0" title="x^{2}+6x+8=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Cari dua bilangan yang hasil kalinya 8 dan hasil penjumlahannya 6</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1 x 8 = 8 <span> </span><span> </span><span> 1 + 8 = 9 (Tidak memenuhi)</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>(-1) x (-8) = 8<span> </span><span> -1-8 = -9 ( Tidak memenuhi)</span></span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span>2 x 4 = 8<span> </span><span> </span><span> 2 + 4 = 6 (memenuhi)</span></span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span><span>(-2) x (-4) = 8<span> </span><span> -2-4 = -6 (tidak memenuhi)</span></span></span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span><span><span>Yang memenuhi adalah bilangan 2 dan 4 maka :</span></span></span></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+6x+8=0" title="x^{2}+6x+8=0" /></p>
<p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)\left&space;(&space;x+4&space;\right&space;)=0" title="\left ( x+2 \right )\left ( x+4 \right )=0" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( x+2 \right )=0" /><span style="font-family: verdana; font-size: medium;"> atau </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+4&space;\right&space;)=0" title="\left ( x+4 \right )=0" /></p><p style="text-align: left;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-2" title="x=-2" /><span> </span><span> <span> </span><span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-4" title="x=-4" /></p><div style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+6x+8=0" title="x^{2}+6x+8=0" /><span style="font-family: verdana;"> adalah </span><i style="font-family: verdana;">x = -2</i><span style="font-family: verdana;"> atau </span><i style="font-family: verdana;">x = -4</i><span style="font-family: verdana;"> atau ditulis juga dengan bentuk {-2,-4}</span></span></div><div style="text-align: justify;"><span style="font-family: verdana; font-size: large;"><br /></span></div><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-7x+10=0" title="x^{2}-7x+10=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Cari dua bilangan yang hadil kalinya 10 dan jumlahnya -7</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2 x 5 = 10<span> </span><span> </span><span> 2 + 5 = 7 (tidak memenuhi)</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">(-2) x (-5) = 10 -2 -5 = -7 (memenuhi)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">maka</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-7x+10=0" title="x^{2}-7x+10=0" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-2&space;\right&space;)\left&space;(&space;x-5&space;\right&space;)=0" title="\left ( x-2 \right )\left ( x-5 \right )=0" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-2&space;\right&space;)=0" title="\left ( x-2 \right )=0" /> <span style="font-family: verdana; font-size: medium;">atau </span><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-5&space;\right&space;)=0" title="\left ( x-5 \right )=0" /><span style="text-align: left;"> </span></p><p style="text-align: justify;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x&space;=&space;2" title="x = 2" /><span> <span> </span><span> </span><span> </span><span> </span></span><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x&space;=&space;5" title="x = 5" /></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}-7x+10=0" title="x^{2}-7x+10=0" /><span style="font-family: verdana;"> adalah {2,5}</span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;"><br /></span></span></p><span style="font-family: verdana; font-size: medium;">
<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">c. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+2x-15=0" title="x^{2}+2x-15=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Cari dua bilangan yang hasil kalinya -15 dan jumlahnya 2</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">(-1) x 15 = -15<span> </span><span> </span><span> -1 + 15 = 14 (tidak memenuhi)</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1 x (-15) = -15<span> </span><span> </span><span> 1 - 15 = -14 (tidak memenuhi)</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">(-3) x 5 = -15<span> </span><span> </span><span> </span><span> -3 + 5 = 2 (memenuhi)</span></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">maka</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+2x-15=0" title="x^{2}+2x-15=0" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-3&space;\right&space;)\left&space;(&space;x+5&space;\right&space;)=0" title="\left ( x-3 \right )\left ( x+5 \right )=0" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-3&space;\right&space;)=0" title="\left ( x-3 \right )=0" /><span style="font-family: verdana; font-size: medium;"> atau </span><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+5&space;\right&space;)=0" title="\left ( x+5 \right )=0" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=3" title="x=3" /><span> </span><span style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-5" title="x=-5" /></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+2x-15=0" title="x^{2}+2x-15=0" /><span style="font-family: verdana;"> adalah {3,-5} </span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;"><br /></span></span></p><p style="text-align: justify;"><b style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Memfaktorkan bentuk persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0,a\neq 1" title="ax^{2}+bx+c=0,a\neq 1" /></b></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Langkah-langah memfaktorkan</span></p><p style="text-align: left;"></p><ol style="text-align: left;"><li><span style="font-family: verdana; font-size: medium;">Kalikan a dan c</span></li><li><span style="font-family: verdana; font-size: medium;">Cari dua bilangan yang hasil kalinya ac dan jumlahnya b</span></li></ol>
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<span style="font-family: verdana; font-size: medium;"><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><b>Contoh 2</b></span><p></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Dengan cara memfaktorkan, tentukan akar-akar dari persamaan kuadrat berikut</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}+5x-2=0" title="3x^{2}+5x-2=0" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;2x^{2}-x-10=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-x-10=0" title="2x^{2}-x-10=0" /></a></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">c. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;3x^{2}-25x+42=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-25x+42=0" title="3x^{2}-25x+42=0" /></a></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif penyelesaian</b></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}+5x-2=0" style="font-family: "Times New Roman"; font-size: medium;" title="3x^{2}+5x-2=0" /></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Kalikan 3 dan -2</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">3 x (-2) = -6</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Cari dua bilangan yang hasil kalinya -6 dan jumlahnya 5</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">1 x (-6) = -6 <span> </span><span> </span><span> 1 - 6 = -5 (tidak memenuhi)</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>(-1) x 6 = -6<span> </span><span> </span><span> -1 + 6 = 5 (memenuhi)</span></span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">2 x (-3) = -6<span> </span><span> </span><span> 2 - 3 = -1 (tidak memenuhi)</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>(-2) x 3 = -6<span> </span><span> </span><span> -2 + 3 = 1 (tidak memenuhi)</span></span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span><span>maka</span></span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span><span>(Perhatikan langkah alternatif 1 menggunakan 5x =-x + 6x berikut)</span></span></span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}+5x-2=0" title="3x^{2}+5x-2=0" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-x+6x-2=0" title="3x^{2}-x+6x-2=0" /> <span style="font-family: verdana; font-size: medium;">(perhatikan 5x diubah menjadi -x + 6x)</span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x^{2}-x&space;\right&space;)+\left&space;(6x-2&space;\right&space;)=0" title="\left ( 3x^{2}-x \right )+\left (6x-2 \right )=0" /> <span style="font-family: verdana; font-size: medium;">(perhatikan penggabungan)</span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x\left&space;(&space;3x-1&space;\right&space;)+2\left&space;(&space;3x-1&space;\right&space;)=0" title="x\left ( 3x-1 \right )+2\left ( 3x-1 \right )=0" /> <span style="font-family: verdana; font-size: medium;">(perhatikan pemfaktoran)</span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)\left&space;(&space;3x-1&space;\right&space;)=0" title="\left ( x+2 \right )\left ( 3x-1 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( x+2 \right )=0" /> <span> </span><span> </span><span style="font-family: verdana; font-size: medium;">atau </span>
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x-1&space;\right&space;)=0" title="\left ( 3x-1 \right )=0" /></p><p style="text-align: left;">
<span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-2" title="x=-2" /><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x=1" title="3x=1" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{1}{3}" title="x=\frac{1}{3}" /><span> </span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">(Perhatikan langkah alternatif 2 menggunakan 5x =6x - x berikut)</span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}+5x-2=0" title="3x^{2}+5x-2=0" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}+6x-x-2=0" title="3x^{2}+6x-x-2=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x^{2}+6x&space;\right&space;)-\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( 3x^{2}+6x \right )-\left ( x+2 \right )=0" /> <span style="font-family: verdana; font-size: medium;">(Perhatikan perubahan tanda)</span></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x\left&space;(&space;x+2&space;\right&space;)-\left&space;(&space;x+2&space;\right&space;)=0" title="3x\left ( x+2 \right )-\left ( x+2 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x-1&space;\right&space;)\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( 3x-1 \right )\left ( x+2 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x-1&space;\right&space;)=0" title="\left ( 3x-1 \right )=0" /> <span style="font-family: verdana; font-size: medium;">atau </span>
<a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( x+2 \right )=0" /></a></p><p style="text-align: left;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x=1" title="3x=1" /> <span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-2" title="x=-2" /></p><p style="text-align: left;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{1}{3}" title="x=\frac{1}{3}" /></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}+5x-2=0" title="3x^{2}+5x-2=0" /><span style="font-family: verdana;"> adalah </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;\frac{1}{3},-2&space;\right&space;\}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;\frac{1}{3},-2&space;\right&space;\}" title="\left \{ \frac{1}{3},-2 \right \}" /></a></span></p><p style="text-align: left;"><br /></p><span style="font-family: verdana; font-size: medium;">
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. </span> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-x-10=0" title="2x^{2}-x-10=0" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Kalikan 2 dan -10</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">2 x (-10) = -20</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Cari dua bilangan yang hasil kalinya -20 dan jumlahnya -1</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">(-4) x 5 = -20 <span> </span><span> -4 + 5 = 1 (tidak memenuhi)</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span>4 x (-5) = -20<span> </span><span> 4 - 5 = -1 (memenuhi)</span></span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><span><span>Maka</span></span></span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-x-10=0" title="2x^{2}-x-10=0" /></p>
<p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}+4x-5x-10=0" title="2x^{2}+4x-5x-10=0" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;2x^{2}+4x&space;\right&space;)-\left&space;(&space;5x+10&space;\right&space;)=0" title="\left ( 2x^{2}+4x \right )-\left ( 5x+10 \right )=0" /></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x\left&space;(&space;x+2&space;\right&space;)-5\left&space;(&space;x+2&space;\right&space;)=0" title="2x\left ( x+2 \right )-5\left ( x+2 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;2x-5&space;\right&space;)\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( 2x-5 \right )\left ( x+2 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;2x-5&space;\right&space;)=0" title="\left ( 2x-5 \right )=0" /><span style="font-family: verdana; font-size: medium;"> atau </span>
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+2&space;\right&space;)=0" title="\left ( x+2 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x=5" title="2x=5" /><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-2" title="x=-2" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{5}{2}" title="x=\frac{5}{2}" /></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}-x-10=0" title="2x^{2}-x-10=0" /><span style="font-family: verdana;"> adalah </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;-2,\frac{5}{2}&space;\right&space;\}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;-2,\frac{5}{2}&space;\right&space;\}" title="\left \{ -2,\frac{5}{2} \right \}" /></a></span></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">c. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;3x^{2}-25x+42=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-25x+42=0" title="3x^{2}-25x+42=0" /></a></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-18x-7x+42=0" title="3x^{2}-18x-7x+42=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x^{2}-18x&space;\right&space;)-\left&space;(&space;7x-42&space;\right&space;)=0" title="\left ( 3x^{2}-18x \right )-\left ( 7x-42 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x\left&space;(&space;x-6&space;\right&space;)-7\left&space;(&space;x-6&space;\right&space;)=0" title="3x\left ( x-6 \right )-7\left ( x-6 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x-7&space;\right&space;)\left&space;(&space;x-6&space;\right&space;)=0" title="\left ( 3x-7 \right )\left ( x-6 \right )=0" /></p><p style="text-align: left;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;3x-7&space;\right&space;)=0" title="\left ( 3x-7 \right )=0" /> <span style="font-family: verdana; font-size: medium;">atau </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-6&space;\right&space;)=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x-6&space;\right&space;)=0" title="\left ( x-6 \right )=0" /></a></p><p style="text-align: left;"><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x=7" title="3x=7" /><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=6" title="x=6" /></p><p style="text-align: left;">
<span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=\frac{7}{3}" title="x=\frac{7}{3}" /></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: verdana;">Jadi akar dari persamaan </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;3x^{2}-25x+42=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3x^{2}-25x+42=0" title="3x^{2}-25x+42=0" /></a><span style="font-family: verdana;"> adalah </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;\frac{7}{3},6&space;\right&space;\}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;\{&space;\frac{7}{3},6&space;\right&space;\}" title="\left \{ \frac{7}{3},6 \right \}" /></a></span></p></span></span></span>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-8595248077127986602.post-11803985354776877052021-08-08T16:34:00.034+08:002021-08-09T11:33:55.335+08:00Menentukan Akar Persamaan Kuadrat Dengan Melengkapkan Kuadrat Sempurna | Matematika SMP/MTs Kelas 9<p><span style="font-family: verdana; font-size: medium;"><b></b></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana; font-size: medium;"><b></b></span></div><span style="font-family: verdana; font-size: medium;"><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx6XUI3flrrB-N-BLnf0JKZ5GY0A9LHrO52e7z6l7g-d7gb0v6gxp85QVc42Nd8u16DNNMC1-16ETxqW4PpjmvDFVHtp0QCFEOgOZeX7KVZDwiRGj9nKg0yWZSDVWyBBt_kSlLtfDbazU/s500/Desain+tanpa+judul.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="500" height="96" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx6XUI3flrrB-N-BLnf0JKZ5GY0A9LHrO52e7z6l7g-d7gb0v6gxp85QVc42Nd8u16DNNMC1-16ETxqW4PpjmvDFVHtp0QCFEOgOZeX7KVZDwiRGj9nKg0yWZSDVWyBBt_kSlLtfDbazU/w96-h96/Desain+tanpa+judul.png" stile="float:left; margin:5px 9px;" width="96" /></a><b><div style="text-align: left;"><b>Bentuk Umum Persamaan Kuadrat</b></div></b></div></span><p></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" title="ax^{2}+bx+c=0" />, <span style="font-family: verdana; font-size: medium;">dengan</span> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a,b,c\in&space;\mathbb{R},a\neq&space;0" title="a,b,c\in \mathbb{R},a\neq 0" /></p><p><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Menentukan Akar Persamaan Kuadrat Dengan Cara Melengkapkan Kudrat Sempurna</b></span></p><p><span style="font-family: verdana; font-size: medium; text-align: justify;"><br /></span></p><p><span style="font-family: verdana; font-size: medium; text-align: justify;">Inti dari melengkapkan kuadrat sempurna adalah mengubah persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" style="text-align: center;" title="ax^{2}+bx+c=0" /><span style="text-align: justify;"> </span><span style="font-family: verdana; font-size: medium; text-align: justify;">menjadi </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+p&space;\right&space;)^{2}+q=0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+p&space;\right&space;)^{2}+q=0" title="\left ( x+p \right )^{2}+q=0" /></a></p><span style="font-family: verdana; font-size: medium;"><div style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Untuk membentuk <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;ax^{2}+bx+c=0" style="font-family: "Times New Roman"; font-size: medium; text-align: center;" title="ax^{2}+bx+c=0" /> menjadi kuadrat sempurna maka koefesien dari</span><span style="font-family: verdana; font-size: large;"> </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x^{2}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}" title="x^{2}" /></a> <span style="font-family: verdana; font-size: medium;">harus 1 sehingga diperoleh </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=0" style="font-family: "Times New Roman"; font-size: medium; text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=0" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=0" /></a></div></span><div><div><p></p><p><span style="font-family: verdana; font-size: medium;">Untuk mencari nilai p dan q ikuti langkah berikut</span></p><p><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=\left&space;(&space;x+p&space;\right&space;)^{2}+q" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=\left&space;(&space;x+p&space;\right&space;)^{2}+q" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=\left ( x+p \right )^{2}+q" /></a></p><p><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+2px+p^{2}+q" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+2px+p^{2}+q" title="x^{2}+\frac{b}{a}x+\frac{c}{a}=x^{2}+2px+p^{2}+q" /></a></p><p><span style="font-family: verdana; font-size: medium;">Dari langkah diatas diperoleh</span></p><p><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{b}{a}=2p" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{b}{a}=2p" title="\frac{b}{a}=2p" /></a></p><p><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;p=\frac{b}{2a}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;p=\frac{b}{2a}" title="p=\frac{b}{2a}" /></a></p><p><span style="font-family: verdana; font-size: medium;">dan</span></p><p><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{c}{a}=p^{2}+q" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{c}{a}=p^{2}+q" title="\frac{c}{a}=p^{2}+q" /></a></p><p><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q=\frac{c}{a}-p^{2}" title="q=\frac{c}{a}-p^{2}" /></p><p><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;q=\frac{c}{a}-\left&space;(&space;\frac{b}{2a}&space;\right&space;)^{2}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;q=\frac{c}{a}-\left&space;(&space;\frac{b}{2a}&space;\right&space;)^{2}" title="q=\frac{c}{a}-\left ( \frac{b}{2a} \right )^{2}" /></a></p><p><br /></p><p><span style="font-family: verdana; font-size: medium;"><b>Contoh 1</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan cara melengkapkan kuadrat sempurna tentukan akar dari persamaan kuadrat berikut. </span></p><p><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+8x+12=0" title="x^{2}+8x+12=0" /></p><p><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}+6x+3=0" title="2x^{2}+6x+3=0" /></p><p><span style="font-family: verdana; font-size: medium;">Alternatif penyelesaian</span></p><p><span style="font-family: verdana; font-size: medium;">a. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+8x+12=0" title="x^{2}+8x+12=0" /></p><p><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+8x=-12" title="x^{2}+8x=-12" /></p><p style="text-align: justify;"><span><span style="font-family: verdana; font-size: medium;">Bagilah koefesien x dengan 2 sehingga diperoleh </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{8}{2}=4" title="\frac{8}{2}=4" /></p></div></div>
<p style="text-align: left;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+8x+4^{2}=-12+4^{2}" title="x^{2}+8x+4^{2}=-12+4^{2}" /></p><div><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+4&space;\right&space;)^{2}=-12+16" title="\left ( x+4 \right )^{2}=-12+16" /></div><p style="text-align: left;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+4&space;\right&space;)^{2}=2" title="\left ( x+4 \right )^{2}=2" /></p><p style="text-align: justify;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+4&space;\right&space;)=\pm&space;\sqrt{2}" title="\left ( x+4 \right )=\pm \sqrt{2}" /></p><p style="text-align: justify;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-4&space;\pm&space;\sqrt{2}" title="x=-4 \pm \sqrt{2}" /></p><p style="text-align: left;"> <span style="font-family: verdana; font-size: medium;"> <span>Jadi akar dari </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+8x+12=0" title="x^{2}+8x+12=0" /><span> adalah</span> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-4+\sqrt{2}" title="x_{1}=-4+\sqrt{2}" /> <span>atau </span> <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}=-4-\sqrt{2}" title="x_{2}=-4-\sqrt{2}" /></span></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">b. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}+6x+3=0" title="2x^{2}+6x+3=0" /></p><p style="text-align: left;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{2}{2}x^{2}+\frac{6}{2}+\frac{3}{2}=0" title="\frac{2}{2}x^{2}+\frac{6}{2}+\frac{3}{2}=0" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{2}{2}x^{2}+\frac{6}{2}+\frac{3}{2}=0" title="\frac{2}{2}x^{2}+\frac{6}{2}+\frac{3}{2}=0" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+3x+\frac{3}{2}=0" title="x^{2}+3x+\frac{3}{2}=0" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+3x=-\frac{3}{2}" title="x^{2}+3x=-\frac{3}{2}" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+3x+\left&space;(&space;\frac{3}{2}&space;\right&space;)^{2}=-\frac{3}{2}+\left&space;(&space;\frac{3}{2}&space;\right&space;)^{2}" title="x^{2}+3x+\left ( \frac{3}{2} \right )^{2}=-\frac{3}{2}+\left ( \frac{3}{2} \right )^{2}" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{3}{2}&space;\right&space;)^{2}=-\frac{3}{2}+\frac{9}{4}" title="\left ( x+\frac{3}{2} \right )^{2}=-\frac{3}{2}+\frac{9}{4}" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{3}{2}&space;\right&space;)^{2}=-\frac{6}{4}+\frac{9}{4}" title="\left ( x+\frac{3}{2} \right )^{2}=-\frac{6}{4}+\frac{9}{4}" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{3}{2}&space;\right&space;)^{2}=\frac{3}{4}" title="\left ( x+\frac{3}{2} \right )^{2}=\frac{3}{4}" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x+\frac{3}{2}=\pm&space;\sqrt{\frac{3}{4}}" title="x+\frac{3}{2}=\pm \sqrt{\frac{3}{4}}" /></p><p style="text-align: left;">
<span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x+\frac{3}{2}=\pm&space;\frac{1}{2}&space;\sqrt{3}" title="x+\frac{3}{2}=\pm \frac{1}{2} \sqrt{3}" /></p><p style="text-align: left;"><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{3}{2}&space;\pm&space;\frac{1}{2}&space;\sqrt{3}" title="x=-\frac{3}{2} \pm \frac{1}{2} \sqrt{3}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Jadi akar dari <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2x^{2}+6x+3=0" title="2x^{2}+6x+3=0" /> adalah <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-\frac{3}{2}&space;+&space;\frac{1}{2}&space;\sqrt{3}" title="x_{1}=-\frac{3}{2} + \frac{1}{2} \sqrt{3}" /> atau <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{2}=-\frac{3}{2}&space;-&space;\frac{1}{2}&space;\sqrt{3}" title="x_{2}=-\frac{3}{2} - \frac{1}{2} \sqrt{3}" /></span></p>
<br /><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Contoh 2</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan cara melengkapkan kuadrat sempurna tentukan akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x+6=0" title="x^{2}+5x+6=0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Alternatif Penyelesaian</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Perhatikan koefesien x adalah 5 dan harus dibagi 2 menjadi </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{5}{2}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{5}{2}" title="\frac{5}{2}" /></a>, <span style="font-family: verdana; font-size: medium;">maka persamaan kuadrat diatas menjadi</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x=-6" title="x^{2}+5x=-6" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x=-6" title="x^{2}+5x=-6" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x+\left&space;(&space;\frac{5}{2}&space;\right&space;)^{2}=-6+\left&space;(&space;\frac{5}{2}&space;\right&space;)^{2}" title="x^{2}+5x+\left ( \frac{5}{2} \right )^{2}=-6+\left ( \frac{5}{2} \right )^{2}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(x+&space;\frac{5}{2}&space;\right&space;)^{2}=-6+\frac{25}{4}" title="\left (x+ \frac{5}{2} \right )^{2}=-6+\frac{25}{4}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(x+&space;\frac{5}{2}&space;\right&space;)^{2}=\frac{1}{4}" title="\left (x+ \frac{5}{2} \right )^{2}=\frac{1}{4}" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x+&space;\frac{5}{2}=\pm&space;\sqrt{\frac{1}{4}}" title="x+ \frac{5}{2}=\pm \sqrt{\frac{1}{4}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-&space;\frac{5}{2}\pm&space;\frac{1}{2}" title="x=- \frac{5}{2}\pm \frac{1}{2}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+5x+6=0" title="x^{2}+5x+6=0" /> <span style="font-family: verdana; font-size: medium;">adalah</span><span style="font-family: verdana; font-size: medium;"> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-&space;\frac{5}{2}+\frac{1}{2}=-\frac{4}{2}=-2" title="x_{1}=- \frac{5}{2}+\frac{1}{2}=-\frac{4}{2}=-2" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>atau</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-&space;\frac{5}{2}-\frac{1}{2}=-\frac{6}{2}=-3" title="x_{1}=- \frac{5}{2}-\frac{1}{2}=-\frac{6}{2}=-3" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><b><span style="font-family: verdana; font-size: medium;">Contoh 3</span></b></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Tentukan akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x-6=0" title="x^{2}+x-6=0" /><span style="font-family: verdana; font-size: large;"> </span><span style="font-family: verdana; font-size: medium;">dengan melengkapkan kuadrat sempurna.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif penyelesaian</b></span></p>
<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Perhatikan koefesien dari x adalah 1, jika dibagi 2 menjadi </span><span style="font-family: verdana; font-size: medium;"> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{2}" title="\frac{1}{2}" /><span style="font-family: verdana; font-size: medium;"> maka persamaan kuadrat tersebut menjadi</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x-6=0" style="text-align: left;" title="x^{2}+x-6=0" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x=6" title="x^{2}+x=6" /></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x+\left&space;(&space;\frac{1}{2}&space;\right&space;)^{2}=6+\left&space;(&space;\frac{1}{2}&space;\right&space;)^{2}" title="x^{2}+x+\left ( \frac{1}{2} \right )^{2}=6+\left ( \frac{1}{2} \right )^{2}" /></p><p style="text-align: justify;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{1}{2}&space;\right&space;)^{2}=6+\frac{1}{4}" title="\left ( x+\frac{1}{2} \right )^{2}=6+\frac{1}{4}" /></p><p style="text-align: justify;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;x+\frac{1}{2}&space;\right&space;)^{2}=\frac{25}{4}" title="\left ( x+\frac{1}{2} \right )^{2}=\frac{25}{4}" /></p><p style="text-align: justify;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x+\frac{1}{2}=\pm&space;\sqrt{\frac{25}{4}}" title="x+\frac{1}{2}=\pm \sqrt{\frac{25}{4}}" /></p><p style="text-align: justify;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x+\frac{1}{2}=\pm&space;\frac{5}{2}" title="x+\frac{1}{2}=\pm \frac{5}{2}" /></p><p style="text-align: justify;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x=-\frac{1}{2}\pm&space;\frac{5}{2}" title="x=-\frac{1}{2}\pm \frac{5}{2}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jadi akar dari persamaan kuadrat </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x^{2}+x-6=0" style="text-align: left;" title="x^{2}+x-6=0" /> <span style="font-family: verdana; font-size: medium;">adalah</span></p><p style="text-align: justify;">
<img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-\frac{1}{2}+&space;\frac{5}{2}=\frac{4}{2}=2" title="x_{1}=-\frac{1}{2}+ \frac{5}{2}=\frac{4}{2}=2" /></p><p style="text-align: justify;">
<span style="font-family: verdana; font-size: medium;">atau </span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;x_{1}=-\frac{1}{2}-&space;\frac{5}{2}=-\frac{6}{2}=-3" title="x_{1}=-\frac{1}{2}- \frac{5}{2}=-\frac{6}{2}=-3" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Untuk mempelajari menentukan akar persamaan kuadrat menggunakan rumus ABC bisa dipelajari di <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/menentukan-akar-persamaan-kuadrat.html">LINK INI</a></span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-8595248077127986602.post-83963748495950020002021-08-04T10:14:00.168+08:002021-08-23T20:33:46.244+08:00Pembahasan Soal Bentuk Akar | Matematika SMP/MTs Kelas 9 Semester Ganjil<p><span style="font-family: verdana;"><b><span style="color: red; font-size: large;"></span></b></span></p><div class="separator" style="clear: both; text-align: justify;"><img border="0" data-original-height="500" data-original-width="500" height="20" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6CZlp2_eT3D-HL03Kulf2jYaG6cShhJC1ly-Z6WoVGtwdyq6sd-FziRyDpHnjkpZUce5v7Y_7JN7HqaxsV0_6VzUcyACcLzxti757IxI3VckYr1uZYFpJKA1mYh367jjzj6GELRFewDM/w20-h20/Desain+tanpa+judul.png" stile="float:left; margin:5px 9px;" width="20" /> <b style="font-family: verdana; text-align: left;"><span style="color: red; font-size: large;"><i>Definisi Akar Kuadrat</i></span></b></div><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jika <i>a</i> tidak negatif </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{a}" title="\sqrt{a}" /> <span style="font-family: verdana; font-size: medium;">adalah bilangan tidak negatif yang kuadratnya adalah <i>a</i>.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">atau bisa dituliskan seperti ini</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuilFvTphb354xqHZDoUqT5cpZc1SrJ1NUm2F1WiFI13L5CYCPCYCg5C1KJtekgQPPlMwMoWJeqoW-rYFx_zhfKVLZwEbdin8Fvm3enFE56CdyZuP_LgcHKaGboE3WtaPXlbubjv3bcSk/s292/gambar+4.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="162" data-original-width="292" height="162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuilFvTphb354xqHZDoUqT5cpZc1SrJ1NUm2F1WiFI13L5CYCPCYCg5C1KJtekgQPPlMwMoWJeqoW-rYFx_zhfKVLZwEbdin8Fvm3enFE56CdyZuP_LgcHKaGboE3WtaPXlbubjv3bcSk/s0/gambar+4.PNG" width="292" /></a></div><br /><span style="font-family: verdana; font-size: medium;"><b><i>Cara menaksir nilai suatu akar</i></b></span><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Untuk melakukan taksiran nilai suatu akar dapat dipelajari di link <a href="https://www.sambimatika.my.id/2013/08/menentukan-nilai-akar-dengan-cara.html" target="_blank">INI</a></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Contoh</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan cara taksiran, carilah nilai dari </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{7}" title="\sqrt{7}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Penyelesaian</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{7}" title="\sqrt{7}" /> <span style="font-family: verdana; font-size: medium;">terletak diantara</span> <span eqnedit.php="" face="<a href=" https:="" latex="\dpi{100}&space;\fn_jvn&space;\sqrt{4}=2" target="_blank" www.codecogs.com=""><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{4}=2" title="\sqrt{4}=2" /><span style="font-family: verdana; font-size: medium;"> dan </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{9}=3" title="\sqrt{9}=3" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">7 - 4 = 3</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">9 - 4 = 5</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">maka</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{7}\approx&space;2\frac{3}{5}=\frac{13}{5}=2,6" title="\sqrt{7}\approx 2\frac{3}{5}=\frac{13}{5}=2,6" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jika mengunakan kalkulator didapatkan seperti pada gambar berikut</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifcFKSC71hyphenhyphenV-e7ED7cZ2ALkmjiWxtNeO4fuy7CAQv8C2q-Tuu6V9OyEI3h_Wm6LPPZif5yxEU5IVhffZp-dTSC0qdAyl2ivxaNbOb7Opj_4fNdRTNf5MLJTcllazOQmv8sSNd_pgA20U/s1280/WhatsApp+Image+2021-08-04+at+09.59.17.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="590" data-original-width="1280" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifcFKSC71hyphenhyphenV-e7ED7cZ2ALkmjiWxtNeO4fuy7CAQv8C2q-Tuu6V9OyEI3h_Wm6LPPZif5yxEU5IVhffZp-dTSC0qdAyl2ivxaNbOb7Opj_4fNdRTNf5MLJTcllazOQmv8sSNd_pgA20U/w640-h296/WhatsApp+Image+2021-08-04+at+09.59.17.jpeg" width="640" /></a></div><br /><span style="font-family: verdana; font-size: medium;"><i><b>Sifat-sifat pada bentuk akar</b></i></span><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jika a dan b bilangan positif, maka berlaku</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;b\sqrt{a}+c\sqrt{a}=\left&space;(&space;b+c&space;\right&space;)\sqrt{a}" title="b\sqrt{a}+c\sqrt{a}=\left ( b+c \right )\sqrt{a}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;b\sqrt{a}-c\sqrt{a}=\left&space;(&space;b-c&space;\right&space;)\sqrt{a}" title="b\sqrt{a}-c\sqrt{a}=\left ( b-c \right )\sqrt{a}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{ab}=\sqrt{axb}=\sqrt{a}x\sqrt{b}" title="\sqrt{ab}=\sqrt{axb}=\sqrt{a}x\sqrt{b}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">4. Jika a>0 dan b<0 maka berlaku </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}" title="\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Merasional Penyebut Pembagian bentuk Akar</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{\sqrt{a}}=\frac{1}{a}\sqrt{a},a\neq&space;0" title="\frac{1}{\sqrt{a}}=\frac{1}{a}\sqrt{a},a\neq 0" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{\sqrt{a}+\sqrt{b}}x\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b}}{a-b}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{\sqrt{a}+\sqrt{b}}x\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b}}{a-b}" title="\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{\sqrt{a}+\sqrt{b}}x\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b}}{a-b}" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{1}{\sqrt{a}-\sqrt{b}}x\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}+\sqrt{b}}{a-b}" title="\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{1}{\sqrt{a}-\sqrt{b}}x\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}+\sqrt{b}}{a-b}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">4. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}x\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}\left&space;(&space;\sqrt{a}+\sqrt{b}&space;\right&space;)}{a-b}" title="\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}x\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}\left ( \sqrt{a}+\sqrt{b} \right )}{a-b}" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Pembahasan Soal-Soal</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 1</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Sederhanakan bentuk akar berikut</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{112}" title="\sqrt{112}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif penyelesaian</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Carilah perkalian yang menghasilkan 112 dengan ketentuan salah satu bilangan merupakan bilangan 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17 dan seterusnya dan bilangan yang lain harus bisa diakarkan langsung</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">112 = 2 x 56 (tidak bisa kita gunakan karena 56 tidak bisa diakarkan)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Perkalian dengan 3, 5 dan 6 tidak kita cek karena tidak ada perkalian dengan bilangan bulat positif yang menghasilkan 112</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">112 = 7 x 16 (bisa digunakan karena 16 bisa diakarkan)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">maka </span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{112}=\sqrt{16x7}=\sqrt{16}x\sqrt{7}=4\sqrt{7}" title="\sqrt{112}=\sqrt{16x7}=\sqrt{16}x\sqrt{7}=4\sqrt{7}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{216}=\sqrt{36x6}=\sqrt{36}x\sqrt{6}=6\sqrt{6}" title="\sqrt{216}=\sqrt{36x6}=\sqrt{36}x\sqrt{6}=6\sqrt{6}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{605}=\sqrt{121x5}=\sqrt{121}x\sqrt{5}=11\sqrt{5}" title="\sqrt{605}=\sqrt{121x5}=\sqrt{121}x\sqrt{5}=11\sqrt{5}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">4. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\sqrt{800}=\sqrt{400x2}=\sqrt{400}x\sqrt{2}=20\sqrt{2}" title="\sqrt{800}=\sqrt{400x2}=\sqrt{400}x\sqrt{2}=20\sqrt{2}" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 2</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Sederhanakan bentuk akar berikut</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;9\sqrt{2}+\sqrt{72}-\sqrt{578}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9\sqrt{2}+\sqrt{72}-\sqrt{578}" title="9\sqrt{2}+\sqrt{72}-\sqrt{578}" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9\sqrt{2}+\sqrt{72}-\sqrt{578}=9\sqrt{2}+\sqrt{36x2}-\sqrt{289x2}=9\sqrt{2}+6\sqrt{2}-17\sqrt{2}" title="9\sqrt{2}+\sqrt{72}-\sqrt{578}=9\sqrt{2}+\sqrt{36x2}-\sqrt{289x2}=9\sqrt{2}+6\sqrt{2}-17\sqrt{2}" /></p>
<p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Dengan menggunakan sifat no 1 dan 2 diatas diperoleh</span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"> <span> </span><span> </span><span> </span><span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;9+6-17&space;\right&space;)\sqrt{2}=\left&space;(&space;15-17&space;\right&space;)\sqrt{2}=-2\sqrt{2}" title="=\left ( 9+6-17 \right )\sqrt{2}=\left ( 15-17 \right )\sqrt{2}=-2\sqrt{2}" /></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">2. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;7\sqrt{3}+\sqrt{48}-\sqrt{768}" title="7\sqrt{3}+\sqrt{48}-\sqrt{768}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif penyelesaian</b></span></p><p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;7\sqrt{3}+\sqrt{48}-\sqrt{768}=7\sqrt{3}+\sqrt{16x3}-\sqrt{256x3}=7\sqrt{3}+4\sqrt{3}-16\sqrt{3}" title="7\sqrt{3}+\sqrt{48}-\sqrt{768}=7\sqrt{3}+\sqrt{16x3}-\sqrt{256x3}=7\sqrt{3}+4\sqrt{3}-16\sqrt{3}" /></p><p style="text-align: left;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> </span><span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;7+4-16&space;\right&space;)\sqrt{3}=-5\sqrt{3}" title="=\left ( 7+4-16 \right )\sqrt{3}=-5\sqrt{3}" /></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9\sqrt{5}-\sqrt{125}+\sqrt{720}" title="9\sqrt{5}-\sqrt{125}+\sqrt{720}" /></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p>
<p style="text-align: left;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9\sqrt{5}-\sqrt{125}+\sqrt{720}=9\sqrt{5}-\sqrt{25x5}+\sqrt{144x5}" title="9\sqrt{5}-\sqrt{125}+\sqrt{720}=9\sqrt{5}-\sqrt{25x5}+\sqrt{144x5}" /></p><p style="text-align: left;"><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=9\sqrt{5}-5\sqrt{5}+12\sqrt{5}=\left&space;(&space;9-5+12&space;\right&space;)\sqrt{5}=16\sqrt{5}" title="=9\sqrt{5}-5\sqrt{5}+12\sqrt{5}=\left ( 9-5+12 \right )\sqrt{5}=16\sqrt{5}" /></p><p style="text-align: left;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 3</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bentuk </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{10}{\sqrt{5+1}}" title="\frac{10}{\sqrt{5+1}}" /> <span style="font-family: verdana; font-size: medium;">senilai dengan....</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">A. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{5}{3}\left&space;(&space;\sqrt{5+1}&space;\right&space;)" title="\frac{5}{3}\left ( \sqrt{5+1} \right )" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">B. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{5}{2}\left&space;(&space;\sqrt{5+1}&space;\right&space;)" title="\frac{5}{2}\left ( \sqrt{5+1} \right )" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">C. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{5}{3}\left&space;(&space;\sqrt{5-1}&space;\right&space;)" title="\frac{5}{3}\left ( \sqrt{5-1} \right )" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">D. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{5}{2}\left&space;(&space;\sqrt{5-1}&space;\right&space;)" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{5}{2}\left&space;(&space;\sqrt{5-1}&space;\right&space;)" title="\frac{5}{2}\left ( \sqrt{5-1} \right )" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{10}{\sqrt{5+1}}=\frac{10}{\sqrt{5+1}}x\frac{\sqrt{5+1}}{\sqrt{5+1}}" title="\frac{10}{\sqrt{5+1}}=\frac{10}{\sqrt{5+1}}x\frac{\sqrt{5+1}}{\sqrt{5+1}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{10\left&space;(&space;\sqrt{5+1}&space;\right&space;)}{5+1}" title="=\frac{10\left ( \sqrt{5+1} \right )}{5+1}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{10\left&space;(&space;\sqrt{5+1}&space;\right&space;)}{6}" title="=\frac{10\left ( \sqrt{5+1} \right )}{6}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{5}{3}\sqrt{5+1}" title="=\frac{5}{3}\sqrt{5+1}" /></p><p style="text-align: justify;"><b><span style="font-family: verdana; font-size: medium;">Kunci : A</span></b></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 4</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bilangan yang senilai dengan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{6}{3-\sqrt{7}}" title="\frac{6}{3-\sqrt{7}}" /> <span style="font-family: verdana; font-size: medium;">adalah....</span></p><p style="text-align: justify;"> <span style="font-family: verdana; font-size: medium;">A. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9-3\sqrt{7}" title="9-3\sqrt{7}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">B. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3-3\sqrt{7}" title="3-3\sqrt{7}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">C. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3+3\sqrt{7}" title="3+3\sqrt{7}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">D. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;9+3\sqrt{7}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;9+3\sqrt{7}" title="9+3\sqrt{7}" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{6}{3-\sqrt{7}}=\frac{6}{3-\sqrt{7}}x\frac{3+\sqrt{7}}{3+\sqrt{7}}" title="\frac{6}{3-\sqrt{7}}=\frac{6}{3-\sqrt{7}}x\frac{3+\sqrt{7}}{3+\sqrt{7}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{6\left&space;(&space;3+\sqrt{7}&space;\right&space;)}{9-7}" title="=\frac{6\left ( 3+\sqrt{7} \right )}{9-7}" /></p>
<p style="text-align: left;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{18+6\sqrt{7}}{2}" title="=\frac{18+6\sqrt{7}}{2}" /> </p><p style="text-align: left;"><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=9+3\sqrt{7}" title="=9+3\sqrt{7}" /></p><div><b><span style="font-family: verdana; font-size: medium;">Kunci : D</span></b></div><div><br /></div><div><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 5</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bentuk </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\sqrt{6}}{\sqrt{15}}" title="\frac{\sqrt{6}}{\sqrt{15}}" /> <span style="font-family: verdana; font-size: medium;">senilai dengan....</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">A. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{6}\sqrt{10}" title="\frac{1}{6}\sqrt{10}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>B. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{5}\sqrt{10}" title="\frac{1}{5}\sqrt{10}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>C. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{2}{5}\sqrt{10}" title="\frac{2}{5}\sqrt{10}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="text-align: left;"></span>D. <img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{3}{5}\sqrt{10}" title="\frac{3}{5}\sqrt{10}" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Pembahasan</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\sqrt{6}}{\sqrt{15}}=\frac{\sqrt{6}x\sqrt{15}}{15}" title="\frac{\sqrt{6}}{\sqrt{15}}=\frac{\sqrt{6}x\sqrt{15}}{15}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{\sqrt{90}}{15}" title="=\frac{\sqrt{90}}{15}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{3\sqrt{10}}{15}" title="=\frac{3\sqrt{10}}{15}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{\sqrt{10}}{5}" title="=\frac{\sqrt{10}}{5}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{1}{5}\sqrt{10}" title="=\frac{1}{5}\sqrt{10}" /></p><p style="text-align: justify;"><b><span style="font-family: verdana; font-size: medium;">Kunci : B</span></b></p><p style="text-align: justify;"><b><span style="font-family: verdana; font-size: medium;"><br /></span></b></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Selanjutnya untuk mempelajari pembahasan soal-soal ulangan harian materi bilangan berpangkat dan bentuk akar silahkan klik <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-soal-ulangan-harian-bilangan.html" target="">LINK INI</a>. </span></p></div>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0tag:blogger.com,1999:blog-8595248077127986602.post-88627527135757342182021-08-03T20:06:00.297+08:002021-08-21T00:05:52.335+08:00Pembahasan Soal Perpangkatan | Matematika SMP/MTs Kelas 9 Semester Ganjil<p style="text-align: left;"><i style="color: red; font-family: verdana; text-align: justify;"><b style="background-color: #04ff00;"><span style="font-size: large;">Definisi pangkat bulat positif</span></b></i></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jika a bilangan riil dan n adalah bilangan bulat positif (bilangan asli), maka</span></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBDB0Nhn8RdRw3F0nrykeNwpxQ9vlB5iG046ayIp2njsIFXXqO6E4eCM9i24R4fMy71Kwxz_Y0_UeRggKyQmXjYvOsxyRZdrZohhC9nGvJky5JliixrvQT4dsMneTf6krLn8dDSuYeO9A/s270/gambar+1.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="97" data-original-width="270" height="97" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBDB0Nhn8RdRw3F0nrykeNwpxQ9vlB5iG046ayIp2njsIFXXqO6E4eCM9i24R4fMy71Kwxz_Y0_UeRggKyQmXjYvOsxyRZdrZohhC9nGvJky5JliixrvQT4dsMneTf6krLn8dDSuYeO9A/s0/gambar+1.PNG" width="270" /></a></div><br /><div style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Sifat-sifat bilangan berpangkat</span></div><div style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Jika a bilangan riil, n,m bilangan bulat positif, maka</span></div><div style="text-align: justify;"><p></p><p></p><p></p><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a^{m}xa^{n}=a^{m+n}" style="font-family: verdana; font-size: large;" title="a^{m}xa^{n}=a^{m+n}" /><br /><p></p><p></p><p></p><span style="font-family: verdana; font-size: medium;">2. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;a^{m}&space;\right&space;)^{}=a^{mn}" title="\left ( a^{m} \right )^{}=a^{mn}" /><br /><p></p><p></p><p></p><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;a.b&space;\right&space;)^{m}=a^{m}b^{m}" title="\left ( a.b \right )^{m}=a^{m}b^{m}" /><br /><p></p><p></p><p></p><p></p><span style="font-family: verdana; font-size: medium;">4. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{a^{m}}{a^{n}}=a^{m-n}" title="\frac{a^{m}}{a^{n}}=a^{m-n}" />, <span style="font-family: verdana; font-size: medium;">dengan <i>m>n</i></span><br /><p></p><span style="font-family: verdana; font-size: medium;">5. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}" title="\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}" />, <span style="font-family: verdana; font-size: medium;">dengan <i>m<n</i></span><br /><p></p><p></p><p></p><span style="font-family: verdana; font-size: medium;">6. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;\frac{a}{b}&space;\right&space;)^{n}=\frac{a^{n}}{b^{n}}" title="\left ( \frac{a}{b} \right )^{n}=\frac{a^{n}}{b^{n}}" /><br /><p></p><p></p><p></p><span style="font-family: verdana; font-size: medium;">7. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a^{0}=1" title="a^{0}=1" />, <span style="font-family: verdana; font-size: medium;">dengan </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a\neq&space;0" title="a\neq 0" /><br /><p></p><span style="font-family: verdana; font-size: medium;">8. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;a^{-n}=\frac{1}{a^{n}}" title="a^{-n}=\frac{1}{a^{n}}" />, <span style="font-family: verdana; font-size: medium;">dengan <i>n>0</i></span><br /><span style="font-family: verdana; font-size: medium;"><br /></span></div><p style="text-align: justify;"><span style="color: red; font-family: verdana; font-size: large;"><b style="background-color: #04ff00;"><i>Soal dan Pembahasan</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 1</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nyatakan perkalian berulang berikut dalam perpangkatan</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-2&space;\right&space;)x\left&space;(&space;-2&space;\right&space;)x\left&space;(&space;-2&space;\right&space;)" title="\left ( -2 \right )x\left ( -2 \right )x\left ( -2 \right )" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif Penyelesaian</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Berdasarkan definisi perpangkatan diatas, maka</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-2&space;\right&space;)x\left&space;(&space;-2&space;\right&space;)x\left&space;(&space;-2&space;\right&space;)=\left&space;(&space;-2&space;\right&space;)^{3}" title="\left ( -2 \right )x\left ( -2 \right )x\left ( -2 \right )=\left ( -2 \right )^{3}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}" title="\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif Penyelesaian</i></b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}=\left&space;(&space;\frac{1}{5}&space;\right&space;)^{5}" title="\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}x\frac{1}{5}=\left ( \frac{1}{5} \right )^{5}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)" title="\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )" /></a></p><p style="text-align: justify;"><b style="font-family: verdana; font-size: large;"><i>Alternatif Penyelesaian</i></b></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)x\left&space;(&space;-\frac{2}{3}&space;\right&space;)=\left&space;(&space;-\frac{2}{3}&space;\right&space;)^{5}" title="\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )x\left ( -\frac{2}{3} \right )=\left ( -\frac{2}{3} \right )^{5}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">4. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;txtxtxtxt" title="txtxtxtxt" /></p><p style="text-align: justify;"><b style="font-family: verdana; font-size: large;"><i>Alternatif Penyelesaian</i></b></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;txtxtxtxt=t^{5}" title="txtxtxtxt=t^{5}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 2</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nyatakan perpangkatan berikut dalam bentuk perkalian berulang</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;3^{8}=3x3x3x3x3x3x3x3" title="3^{8}=3x3x3x3x3x3x3x3" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;0,83&space;\right&space;)^{4}=\left&space;(&space;0,83&space;\right&space;)x\left&space;(&space;0,83&space;\right&space;)x\left&space;(&space;0,83&space;\right&space;)x\left&space;(&space;0,83&space;\right&space;)" title="\left ( 0,83 \right )^{4}=\left ( 0,83 \right )x\left ( 0,83 \right )x\left ( 0,83 \right )x\left ( 0,83 \right )" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-\frac{1}{4}&space;\right&space;)^{4}=\left&space;(&space;-\frac{1}{4}&space;\right&space;)x\left&space;(&space;-\frac{1}{4}&space;\right&space;)x\left&space;(&space;-\frac{1}{4}&space;\right&space;)x\left&space;(&space;-\frac{1}{4}&space;\right&space;)" title="\left ( -\frac{1}{4} \right )^{4}=\left ( -\frac{1}{4} \right )x\left ( -\frac{1}{4} \right )x\left ( -\frac{1}{4} \right )x\left ( -\frac{1}{4} \right )" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">4. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;-\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}=-\left&space;(&space;\frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4}&space;\right&space;)" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;-\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}=-\left&space;(&space;\frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4}&space;\right&space;)" title="-\left ( \frac{1}{4} \right )^{4}=-\left ( \frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4} \right )" /></a></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 3</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Tentukan hasil dari perpangkatan berikut</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;2^{8}=2x2x2x2x2x2x2x2=256" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2^{8}=2x2x2x2x2x2x2x2=256" title="2^{8}=2x2x2x2x2x2x2x2=256" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;(&space;0,02&space;\right&space;)^{2}=0,0004" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;0,02&space;\right&space;)^{2}=0,0004" title="\left ( 0,02 \right )^{2}=0,0004" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;\frac{1}{3}&space;\right&space;)^{3}=\frac{1}{3}x\frac{1}{3}x\frac{1}{3}=\frac{1}{27}" title="\left ( \frac{1}{3} \right )^{3}=\frac{1}{3}x\frac{1}{3}x\frac{1}{3}=\frac{1}{27}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">4. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;-\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}=-\left&space;(&space;\frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4}&space;\right&space;)=-\left&space;(&space;\frac{1}{256}&space;\right&space;)=-\frac{1}{256}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;-\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}=-\left&space;(&space;\frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4}&space;\right&space;)=-\left&space;(&space;\frac{1}{256}&space;\right&space;)=-\frac{1}{256}" title="-\left ( \frac{1}{4} \right )^{4}=-\left ( \frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4} \right )=-\left ( \frac{1}{256} \right )=-\frac{1}{256}" /></a></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 4</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nyatakan bilangan berikut dalam perpangkatan dengan basis 10</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;1.000=10^{3}" title="1.000=10^{3}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">(Tips : pangkat = banyak nol)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;100.000=10^{5}" title="100.000=10^{5}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;1000.000=10^{6}" title="1000.000=10^{6}" /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 5</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nyatakan bilangan berikut dalam perpangkatan basis 2</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. 256</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif Penyelesaian</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan menggunakan diagram pohon diperoleh</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1oViLDGu1DazT7wxvaNdcb672C57U_WTmk6rRJIhrIeyiCGysGTRT7eQ1JD934j8OcCfH4-vcNFEvzGnzFp23eZ81hj56TXOo36GmZJRdHbUejDqQZNFUhxuIBVhcG6i4AqVPUZAn05Y/s651/gambar+2.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="557" data-original-width="651" height="343" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1oViLDGu1DazT7wxvaNdcb672C57U_WTmk6rRJIhrIeyiCGysGTRT7eQ1JD934j8OcCfH4-vcNFEvzGnzFp23eZ81hj56TXOo36GmZJRdHbUejDqQZNFUhxuIBVhcG6i4AqVPUZAn05Y/w400-h343/gambar+2.PNG" width="400" /></a></div><br /><span style="font-family: verdana; font-size: medium;">Dari diagram pohon diatas kita bisa tuliskan</span><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2^{8}" title="2^{8}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. 64</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan cara yang sama dengan penyelesaian soal no 1 kita dapatkan</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">64 = 2 x 2 x 2 x 2 x 2 x 2 = </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2^{6}" title="2^{6}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. 1.048.576</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan cara yang sama dengan penyelesaian soal no 1 kita dapatkan</span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana;">1.048.576 = 2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 x </span><span style="font-family: verdana;">2 = </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;2^{20}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2^{20}" title="2^{20}" /></a></span></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 6</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Nyatakan bilangan berikut dalam perpangkatan basis 5</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. 5 = </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;5^{1}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;5^{1}" title="5^{1}" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. 625</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif Penyelesaian</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Dengan menggunakan diagram pohon diperoleh</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq4yOnuTHTKMz5beKO-CGBJyqZqYQ-VrKX6wKPxF93KJe5m0W7DBXz6sr8hFaobFxtDoVclSUrOJUDHH-U3uQJej29kpBYw6YCkil6PEO17VhPpAmI1YgPFMmwADaet0nhsbn7WyWOcgA/s349/gambar+3.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="259" data-original-width="349" height="237" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq4yOnuTHTKMz5beKO-CGBJyqZqYQ-VrKX6wKPxF93KJe5m0W7DBXz6sr8hFaobFxtDoVclSUrOJUDHH-U3uQJej29kpBYw6YCkil6PEO17VhPpAmI1YgPFMmwADaet0nhsbn7WyWOcgA/w320-h237/gambar+3.PNG" width="320" /></a></div><span style="font-family: verdana; font-size: medium; text-align: left;">Dari diagram pohon diatas kita bisa tuliskan</span><p></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana; text-align: left;">625 = 5 x 5 x 5 x 5 = </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;5^{4}" title="5^{4}" /><span style="font-family: verdana; text-align: left;"> </span></span></p><p style="text-align: justify;"><span style="font-size: medium;"><span style="font-family: verdana; text-align: left;">3. 15.625</span></span></p><p style="text-align: left;"><span style="font-family: verdana; font-size: medium;">Dengan cara yang sama dengan penyelesaian soal no 2 diperoleh</span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: verdana;">15.625 = 5 x </span><span style="font-family: verdana;">5 x </span><span style="font-family: verdana;">5 x </span><span style="font-family: verdana;">5 x </span><span style="font-family: verdana;">5 x </span><span style="font-family: verdana;">5 = </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;5^{6}" title="5^{6}" /></span></p><p style="text-align: left;"><span style="font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 7</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Tentukan hasil operasi berikut ini</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;5+3x2^{4}" title="5+3x2^{4}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif penyelesaian</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Kita harus ingat kembali urutan penyelesaian suatu operasi yaitu perkalian, pembagian, penjumlahan atau pengurangan. Dan yang perlu diingat juga selesaikan terlebih dahulu operasi yang ada di dalam kurung.</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;5+3x2^{4}=5+3x2x2x2x2=5+48=53" title="5+3x2^{4}=5+3x2x2x2x2=5+48=53" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\frac{1}{2}\left&space;(&space;6^{3}-4^{2}&space;\right&space;)=\frac{1}{2}\left&space;(&space;6x6x6-4x4&space;\right&space;)=\frac{1}{2}\left&space;(&space;216-16&space;\right&space;)=\frac{1}{2}200=100" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{2}\left&space;(&space;6^{3}-4^{2}&space;\right&space;)=\frac{1}{2}\left&space;(&space;6x6x6-4x4&space;\right&space;)=\frac{1}{2}\left&space;(&space;216-16&space;\right&space;)=\frac{1}{2}200=100" title="\frac{1}{2}\left ( 6^{3}-4^{2} \right )=\frac{1}{2}\left ( 6x6x6-4x4 \right )=\frac{1}{2}\left ( 216-16 \right )=\frac{1}{2}200=100" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">3. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}:-\left&space;(&space;\frac{1}{3}&space;\right&space;)^{2}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}:-\left&space;(&space;\frac{1}{3}&space;\right&space;)^{2}" title="\left ( \frac{1}{4} \right )^{4}:-\left ( \frac{1}{3} \right )^{2}" /></a></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif penyelesaian</i></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bentuk soal diatas bisa juga diubah menjadi</span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\left&space;(&space;\frac{1}{4}&space;\right&space;)^{4}}{-\left&space;(&space;\frac{1}{3}&space;\right&space;)^{2}}=\frac{\frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4}}{-\left&space;(&space;\frac{1}{3}x\frac{1}{3}&space;\right&space;)}=\frac{\frac{1}{256}}{-\frac{1}{9}}=\frac{1}{256}\left&space;(&space;-9&space;\right&space;)=-\frac{9}{256}" title="\frac{\left ( \frac{1}{4} \right )^{4}}{-\left ( \frac{1}{3} \right )^{2}}=\frac{\frac{1}{4}x\frac{1}{4}x\frac{1}{4}x\frac{1}{4}}{-\left ( \frac{1}{3}x\frac{1}{3} \right )}=\frac{\frac{1}{256}}{-\frac{1}{9}}=\frac{1}{256}\left ( -9 \right )=-\frac{9}{256}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><br /></b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 8</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Tentukan nilai x pada persamaan matematika dibawah ini</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">1. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;7^{x}=343" title="7^{x}=343" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b><i>Alternatif penyelesaian</i></b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;7^{x}=343" title="7^{x}=343" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;7^{x}=7^{3}" title="7^{x}=7^{3}" /> (basis ruas kiri dan kanan sudah sama)</p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">x = 3</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">2. </span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;10^{x}=10.000" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;10^{x}=10.000" title="10^{x}=10.000" /></a></p><p style="text-align: justify;"><b style="font-family: verdana; font-size: large;"><i>Alternatif penyelesaian</i></b></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;10^{x}=10^{4}" title="10^{x}=10^{4}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">x = 4</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 9</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Bentuk </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\left&space;(&space;-2&space;\right&space;)^{8}x\left&space;(&space;-2&space;\right&space;)^{3}}{\left&space;(&space;-2&space;\right&space;)^{9}}" title="\frac{\left ( -2 \right )^{8}x\left ( -2 \right )^{3}}{\left ( -2 \right )^{9}}" /> <span style="font-family: verdana; font-size: medium;">jika disederhanakan menjadi....</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">A. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-2&space;\right&space;)^{2}" title="\left ( -2 \right )^{2}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">B. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-2&space;\right&space;)^{-3}" title="\left ( -2 \right )^{-3}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">C. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-2&space;\right&space;)^{12}" title="\left ( -2 \right )^{12}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">D. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\left&space;(&space;-2&space;\right&space;)^{0}" title="\left ( -2 \right )^{0}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{\left&space;(&space;-2&space;\right&space;)^{8}x\left&space;(&space;-2&space;\right&space;)^{3}}{\left&space;(&space;-2&space;\right&space;)^{9}}=\frac{\left&space;(&space;-2&space;\right&space;)^{8+3}}{\left&space;(&space;-2&space;\right&space;)^{9}}" title="\frac{\left ( -2 \right )^{8}x\left ( -2 \right )^{3}}{\left ( -2 \right )^{9}}=\frac{\left ( -2 \right )^{8+3}}{\left ( -2 \right )^{9}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\frac{\left&space;(&space;-2&space;\right&space;)^{11}}{\left&space;(&space;-2&space;\right&space;)^{9}}" title="=\frac{\left ( -2 \right )^{11}}{\left ( -2 \right )^{9}}" /></p><p style="text-align: justify;"><span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> <span> </span></span></span><a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;-2&space;\right&space;)^{11-9}" style="text-align: left;" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;-2&space;\right&space;)^{11-9}" title="=\left ( -2 \right )^{11-9}" /></a><span style="text-align: left;"> </span></p><p style="text-align: justify;"><span> </span><span> </span><span> </span><span> <span> </span><span> </span><span> </span><span> </span></span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=\left&space;(&space;-2&space;\right&space;)^{2}" title="=\left ( -2 \right )^{2}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Kunci : <b>A</b></span></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 10</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Hasil dari </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;27^{\frac{1}{3}}x64^{\frac{1}{6}}" title="27^{\frac{1}{3}}x64^{\frac{1}{6}}" /> <span style="font-family: verdana; font-size: medium;">adalah....</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">A. 6</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">B. 12</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">C. 24</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">D. 30</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;27^{\frac{1}{3}}x64^{\frac{1}{6}}=\left&space;(&space;3^{3}&space;\right&space;)^{\frac{1}{3}}x\left&space;(&space;2^{6}&space;\right&space;)^{\frac{1}{6}}" title="27^{\frac{1}{3}}x64^{\frac{1}{6}}=\left ( 3^{3} \right )^{\frac{1}{3}}x\left ( 2^{6} \right )^{\frac{1}{6}}" /></p><p style="text-align: justify;"><span style="text-align: left;">
</span><span> </span><span> </span><span> </span><span> </span><span> </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;=3x2=6" title="=3x2=6" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Kunci : <b>A</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Soal 11</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Hasil dari </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2^{-3}x2^{-2}=...." title="2^{-3}x2^{-2}=...." /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">A. -32</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">B. -2</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">C. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{64}" title="\frac{1}{64}" /></p><p style="text-align: justify;"><span style="text-align: left;"></span><span style="font-family: verdana; font-size: medium;">D. </span><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;\frac{1}{32}" title="\frac{1}{32}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><b>Alternatif Penyelesaian</b></span></p><p style="text-align: justify;"><img src="https://latex.codecogs.com/gif.latex?\dpi{100}&space;\fn_jvn&space;2^{-3}x2^{-2}=2^{-3-2}=2^{-5}=\frac{1}{2^{5}}=\frac{1}{32}" title="2^{-3}x2^{-2}=2^{-3-2}=2^{-5}=\frac{1}{2^{5}}=\frac{1}{32}" /></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Kunci : <b>D</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;">Selanjutnya untuk mempelajari pembahasan soal bentuk akar, silahkan klik <a href="https://matematikasmpmts.sambimatika.my.id/2021/08/pembahasan-soal-bentuk-akar-matematika.html" target="">LINK INI</a>.</span></p>Nurman Karimhttp://www.blogger.com/profile/05639846116482307841noreply@blogger.com0