Matematika

Pertanyaan

Fast response please :)
Fast response please :)

1 Jawaban

  • 6) 2 . 4^x - 5 . 2^x + 2 = 0
    2 . (2^x)^2 - 5 . 2^x + 2 = 0 ===> misal 2^x = p
    2p^2 - 5p + 2 = 0
    (2p - 1)(p - 2) = 0
    p = 1/2 atau p = 2
    2^x = 2^-1 atau 2^x = 2^1
    x = -1 atau x = 1
    Hasil kali : x1 . x2 = (-1) . 1 = -1

    7) 4^x + 4^-x = 7

    (2^x + 2^-x)^2 = 2^2x + 2 . 2^x . 2^-x + 2^-2x
    (2^x + 2^-x)^2 = 4^x + 2 + 4^-x
    (2^x + 2^-x)^2 = 4^x + 4^-x + 2
    (2^x + 2^-x)^2 = 7 + 2
    (2^x + 2^-x) = √9 = 3

    8^x + 8^-x = (2^x)^3 + (2^-x)^3
    = (2^x + 2^-x)^3 - 3 . 2^x . 2^-x (2^x + 2^-x)
    = (3)^3 - 3 . 1 (3)
    = 27 - 9
    = 18