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

Answer 2

$\frac{x-1}{x}=3\\ \\ x-1=3x\\ \\ 2x=-1\\ \\ \boxed{x=-\frac{1}{2}}\\ \\ \boxed{ \frac{x^2+1}{x^2}=\frac{(\frac{1}{2})^2+1}{(\frac{1}{2})^2}=\frac{\frac{1}{4}+1}{\frac{1}{4}}=\frac{\frac{5}{4}}{\frac{1}{4}}=5}\\ \\ \boxed{ \frac{x^4+1}{x^4}=\frac{(\frac{1}{2})^4+1}{(\frac{1}{2})^4}=\frac{\frac{1}{16}+1}{\frac{1}{16}}=\frac{\frac{17}{16}}{\frac{1}{16}}=17}$