Question

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

Answer 1

Verified answer

Eksponensial


x^(1/2) + x^(-1/2) = 2
x^(1/2) + 1/(x^1/2) = 2

Permisalan x^1/2 = a

a + 1/a = 2

x^(3/2) + x^(-3/2)
= x^( (1/2) • 3) + 1/ ( x^ ( 1/2) •3)
= a³ + 1/a³

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(a + 1/a)² = 2²
(a² + 2 + 1/a²) = 4
(a² + 1/a²) = 4-2 = 2


(a² + 1/a²) ( a + 1/a) = 2 . 2
a³ + a + 1/a + 1/a³ = 4
(a³ + 1/a³) + 2 = 4
(a³ + 1/a³) = 4-2

(a³ + 1/a³) = 2