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Pertanyaan

Jika x 1 , x 2 adalah akar-akar 9 x – 3 x+1 – 3 x+2 – 3⋅3 x+3 + a = 0 yang memenuhi x 1 + x 2 = 3 3 log⁡2, maka a = ....

Jika x1, x2 adalah akar-akar 9x – 3x+1 – 3x+2 – 3⋅3x+3 + a = 0 yang memenuhi x1 + x2 = 3 3log⁡2, maka a = ....

  1. 27

  2. 16

  3. 9

  4. 8

  5. 4

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jika y = 3 x , maka didapat bahwa y 2 – 93y + a = 0 Perhatikan bahwa Pada persamaan kuadrat y 2 – 93y + a = 0, didapat bahwa y 1 ⋅y 2 = a. Sehingga a = 8. Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 9 to the power of straight x minus 3 to the power of straight x plus 1 end exponent minus 3 to the power of straight x plus 2 end exponent minus 3 times 3 to the power of straight x plus 3 end exponent plus straight a end cell equals 0 row cell 9 to the power of straight x minus 3 to the power of straight x times 3 to the power of 1 minus 3 to the power of straight x times 3 squared minus 3 times 3 to the power of straight x times 3 cubed plus straight a end cell equals 0 row cell 9 to the power of straight x minus 3 to the power of straight x times 3 minus 3 to the power of straight x times 9 minus 3 times 3 to the power of straight x times 27 plus straight a end cell equals 0 row cell 9 to the power of straight x minus 3 times 3 to the power of straight x minus 9 times 3 to the power of straight x minus 81 times 3 to the power of straight x plus straight a end cell equals 0 row cell 9 to the power of straight x minus 93 times 3 to the power of straight x plus straight a end cell equals 0 end table end style 

Jika y = 3x, maka didapat bahwa 

y2 – 93y + a = 0

Perhatikan bahwa 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x subscript 1 plus straight x subscript 2 end cell equals cell 3 times log presubscript straight presuperscript 3 invisible function application 2 end cell row cell 3 to the power of straight x subscript 1 plus straight x subscript 2 end exponent end cell equals cell 3 to the power of 3 times log presubscript straight presuperscript 3 invisible function application 2 end exponent end cell row cell 3 to the power of straight x subscript 1 plus straight x subscript 2 end exponent end cell equals cell 3 to the power of log presubscript straight presuperscript 3 invisible function application 2 cubed end exponent end cell row cell 3 to the power of straight x subscript 1 plus straight x subscript 2 end exponent end cell equals cell 3 to the power of log presubscript straight presuperscript 3 invisible function application 8 end exponent end cell row cell 3 to the power of straight x subscript 1 plus straight x subscript 2 end exponent end cell equals 8 row cell 3 to the power of straight x subscript 1 end exponent times 3 to the power of straight x subscript 2 end exponent end cell equals 8 row cell straight y subscript 1 times straight y subscript 2 end cell equals 8 end table end style 

Pada persamaan kuadrat y2 – 93y + a = 0, didapat bahwa y1⋅y2 = a. Sehingga a = 8.

Jadi, jawaban yang tepat adalah D.

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