Fathiyya T
23 Agustus 2023 08:45
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Fathiyya T
23 Agustus 2023 08:45
Pertanyaan
Tentukan akar-akar persamaan kuadrat berikut dengan cara melengkapi kuadrat sempurna
Tentukan akar-akar persamaan kuadrat berikut dengan cara melengkapi kuadrat sempurna
8 dari 10 siswa nilainya naik
dengan paket belajar pilihan
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Sumber W
Community
23 Agustus 2023 09:09
<p>a. x<sup>2</sup> - 64 = 0</p><p> x<sup>2</sup> = 64</p><p> x = ±√64</p><p> x = ±8</p><p> x<sub>1</sub> = -8 atau x<sub>2</sub> = -8</p><p> </p><p>b. x<sup>2</sup> - 6x + 7 = 0</p><p> x<sup>2</sup> - 6x = -7 </p><p> x<sup>2</sup> - 6x + (-6/2)<sup>2</sup> = -7 + (-6/2)<sup>2</sup> </p><p> x<sup>2</sup> - 6x + (-3)<sup>2</sup> = -7 + (-3)<sup>2</sup> </p><p> x<sup>2</sup> - 6x + 9 = -7 + 9</p><p> x<sup>2</sup> - 6x + 9 = 2</p><p> (x - 3)<sup>2</sup> = 2</p><p> x - 3 = ±√2</p><p> x = 3 ± √2</p><p> x<sub>1</sub> = 3 + √2 atau x<sub>2</sub> = 3 - √2</p><p> </p><p>c. 2x<sup>2</sup> + 3x - 20 = 0</p><p> 2x<sup>2</sup> + 3x = 20</p><p> x<sup>2</sup> + 3/2 x = 10 (masing-masing ruang dibagi 2)</p><p> x<sup>2</sup> + 3/2 x + (3/4)<sup>2 </sup>= 10 + (3/4)<sup>2 </sup></p><p> x<sup>2</sup> + 3/2 x + 9/16<sup> </sup>= 10 + 9/16</p><p> x<sup>2</sup> + 3/2 x + 9/16<sup> </sup>= 160/16 + 9/16</p><p> x<sup>2</sup> + 3/2 x + 9/16<sup> </sup>= 169/16</p><p> (x + 3/4)<sup>2</sup> = 169/16</p><p> x + 3/4 = ±√(169/16)</p><p> x + 3/4 = ± 13/4</p><p> x = -3/4 ± 13/4</p><p> x<sub>1</sub> = -3/4 + 13/4 = 10/4 =<strong> 5/2</strong></p><p> atau</p><p> x<sub>2</sub> = -3/4 - 13/4 = -16/4 = <strong>-4</strong></p><p> </p><p> </p><p> </p>
a. x2 - 64 = 0
x2 = 64
x = ±√64
x = ±8
x1 = -8 atau x2 = -8
b. x2 - 6x + 7 = 0
x2 - 6x = -7
x2 - 6x + (-6/2)2 = -7 + (-6/2)2
x2 - 6x + (-3)2 = -7 + (-3)2
x2 - 6x + 9 = -7 + 9
x2 - 6x + 9 = 2
(x - 3)2 = 2
x - 3 = ±√2
x = 3 ± √2
x1 = 3 + √2 atau x2 = 3 - √2
c. 2x2 + 3x - 20 = 0
2x2 + 3x = 20
x2 + 3/2 x = 10 (masing-masing ruang dibagi 2)
x2 + 3/2 x + (3/4)2 = 10 + (3/4)2
x2 + 3/2 x + 9/16 = 10 + 9/16
x2 + 3/2 x + 9/16 = 160/16 + 9/16
x2 + 3/2 x + 9/16 = 169/16
(x + 3/4)2 = 169/16
x + 3/4 = ±√(169/16)
x + 3/4 = ± 13/4
x = -3/4 ± 13/4
x1 = -3/4 + 13/4 = 10/4 = 5/2
atau
x2 = -3/4 - 13/4 = -16/4 = -4
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