Question

Dado x-1/x=3,obtenha o valor numérico de x²+1/x² e x⁴+1/x⁴

Answer 1

x-1/x=3 => x-1=3x => 2x=-1 => x=-1/2
x² + 1/x² = (-1/2)²+(1.(-2))² = -1/4+4 = 17/4;
x⁴+1/x₄ = (-1/2)₄+(1.(2))₄ = -1/16+16 = 255/16