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

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Jawaban terverifikasi

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Sumber W

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23 Agustus 2023 09:09

Jawaban terverifikasi

<p>a. x<sup>2</sup> - 64 = 0</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> = 64</p><p>&nbsp; &nbsp; &nbsp;x = ±√64</p><p>&nbsp; &nbsp; &nbsp;x = ±8</p><p>&nbsp; &nbsp; &nbsp;x<sub>1</sub> = -8 atau x<sub>2</sub> = -8</p><p>&nbsp;&nbsp;</p><p>b. x<sup>2</sup> - 6x + 7 = 0</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> - 6x = &nbsp;-7&nbsp;</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> - 6x + (-6/2)<sup>2</sup> = &nbsp;-7 + (-6/2)<sup>2</sup>&nbsp;</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> - 6x + (-3)<sup>2</sup> = &nbsp;-7 + (-3)<sup>2</sup>&nbsp;</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> - 6x + 9 = &nbsp;-7 + 9</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> - 6x + 9 = &nbsp;2</p><p>&nbsp; &nbsp; &nbsp;(x - 3)<sup>2</sup> = 2</p><p>&nbsp; &nbsp; &nbsp; x - 3 = ±√2</p><p>&nbsp; &nbsp; &nbsp; x = 3 ± √2</p><p>&nbsp; &nbsp; &nbsp; x<sub>1</sub> = 3 + √2 atau x<sub>2</sub> = 3 - √2</p><p>&nbsp;</p><p>c. 2x<sup>2</sup> + 3x - 20 = 0</p><p>&nbsp; &nbsp; &nbsp;2x<sup>2</sup> + 3x &nbsp;= 20</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> + 3/2 x = 10 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(masing-masing ruang dibagi 2)</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> + 3/2 x + (3/4)<sup>2 </sup>= 10 + (3/4)<sup>2&nbsp;</sup></p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> + 3/2 x + 9/16<sup> </sup>= 10 + 9/16</p><p>&nbsp; &nbsp; &nbsp;x<sup>2</sup> + 3/2 x + 9/16<sup> </sup>= 160/16 + 9/16</p><p>&nbsp; &nbsp; &nbsp; x<sup>2</sup> + 3/2 x + 9/16<sup> </sup>= 169/16</p><p>&nbsp; &nbsp; &nbsp; (x + 3/4)<sup>2</sup> = 169/16</p><p>&nbsp; &nbsp; &nbsp; x + 3/4 = ±√(169/16)</p><p>&nbsp; &nbsp; &nbsp; x + 3/4 = ± 13/4</p><p>&nbsp; &nbsp; &nbsp; x = -3/4 ± 13/4</p><p>&nbsp; &nbsp; &nbsp; &nbsp;x<sub>1</sub> = -3/4 + 13/4 = 10/4 =<strong> 5/2</strong></p><p>&nbsp; &nbsp; &nbsp; &nbsp; atau</p><p>&nbsp; &nbsp; &nbsp; &nbsp;x<sub>2</sub> = &nbsp;-3/4 - 13/4 = -16/4 = <strong>-4</strong></p><p>&nbsp; &nbsp; &nbsp;</p><p>&nbsp;</p><p>&nbsp;</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)

     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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