Question

x + x–¹= 4, Calcular
x³ + x–³.por favor ayuda :(, :(

Answer 1

Elevemos al cubo.

(x + 1/x)³ = 4³ = 64; quitamos el paréntesis:

x³ + 3 x² / x + 3 x / x² + 1/x³ = 64

Pero 3 x² / x + 3 x / x² = 3 x + 3 / x = 3 (x + 1/x) = 3 . 4 = 12

x³ + 12 + 1/x³ = 64

Finalmente x³ + 1/x³ = 64 - 12 = 52

Mateo