Question

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

Answer 1

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