Question

X+1/x=1
x^{10}+x^{-10}=?
mohon di bantu ya ka... :)

Answer 1

X + 1/x = 1
kuadratkan:
x² + 1/x² + 2 = 1
x² + 1/x² = -1
kuadratkan lagi
x⁴ + 1/x⁴ + 2 = -1
x⁴ + 1/x⁴ = -3
kuadratkan lagi
x⁸ + 1/x⁸ + 2 = -3
x⁸ + 1/x⁸ = -5

(x² + 1/x²)(x⁸ + 1/x⁸) = 5
x¹⁰ + 2/x⁶ + 1/x¹⁰ = 5
x¹⁰ + 1/x¹⁰ = 5 - 2/x⁶
sepertinya bgtu