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Pertanyaan

Jika x 1 ,x 2 adalah akar-akar 2 5 x − 2. 5 x + 1 − 5 x + a = 0 dimana x 1 ​ + x 2 ​ = 2. 5 ​ lo g 2 + 1 , maka a = ....

Jika x1,x2 adalah akar-akar  dimana , maka a = ....

  1. 30

  2. 25

  3. 20

  4. 10

  5. 5

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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begin mathsize 14px style text i) Sederhanakan bentuk yang dapat disederhanakan end text  25 to the power of x minus 2 bullet 5 to the power of x plus 1 end exponent minus 5 to the power of x plus a equals 0  open parentheses 5 squared close parentheses to the power of x minus 2 bullet 5 to the power of x bullet 5 to the power of 1 minus 5 to the power of x plus a equals 0  5 to the power of 2 x end exponent minus 10 bullet 5 to the power of x minus 5 to the power of x plus a equals 0  5 to the power of 2 x end exponent minus 11 bullet 5 to the power of x plus a equals 0    text ii) Misalkan  end text y equals 5 to the power of x  text Sehingga end text  y squared minus 11 y plus a equals 0  text Ingat! Jika persamaan kuadrat end text space a x squared plus b x plus c equals 0 text  memiliki akar-akar  end text x subscript 1 space text dan end text space x subscript 2 comma space text maka end text  x subscript 1 plus x subscript 2 equals negative b over a  x subscript 1 x subscript 2 equals c over a  text Sehingga jika persamaan kuadrat  end text y squared minus 11 y plus a equals 0 space memiliki space akar minus akar space y subscript 1 space text dan end text space y subscript 2 comma space text maka end text  y subscript 1 y subscript 2 equals a    text iii) Substitusikan kembali  end text y equals 5 to the power of x  y subscript 1 y subscript 2 equals a  5 to the power of x subscript 1 end exponent 5 to the power of x subscript 2 end exponent equals a  5 to the power of x subscript 1 plus x subscript 2 end exponent equals a  text Diketahui  end text x subscript 1 plus x subscript 2 equals 2 bullet log presubscript space presuperscript 5 space 2 plus 1 text  maka end text  5 to the power of 2 bullet log presubscript space presuperscript 5 space 2 plus 1 end exponent equals a  5 to the power of log presubscript space presuperscript 5 space 2 squared plus 1 end exponent equals a  5 to the power of log presubscript space presuperscript 5 space 2 squared end exponent bullet 5 to the power of 1 equals a  2 squared bullet 5 equals a  a equals 20 end style

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