Matematika

Pertanyaan

Jika x^1/2+x^-1/2 = 2 maka x^3/2+x^-3/2 sama dengan

1 Jawaban

  • x^1/2 + x^-1/2 = 2
    (x^1/2 + x^-1/2)^3 = 2^3
    (x^1/2 + x^-1/2)^2 (x^1/2 + x^-1/2) = 8
    (x + 2 + x^-1) (x^1/2 + x^-1/2) = 8
    x^3/2 + x^1/2 + 2x^1/2 + 2x^-1/2 + x^-1/2 + x^-3/2 = 8
    x^3/2 + x^-3/2 + 3x^1/2 + 3x^-1/2 = 8
    x^3/2 + x^-3/2 + 3(x^1/2 + x^-1/2) = 8
    x^3/2 + x^-3/2 + 3(2) = 8
    x^3/2 + x^-3/2 + 6 = 8
    x^3/2 + x^-3/2 = 2

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