Question

Si x - 1/x = 4
x3 - 1/x3 = 5

Calcule x2 + 1/x2

Answer 1

Tienes lo siguiente:
$x^3- (\frac{1}{x})^3=(x- \frac{1}{x} ) (x^2+x( \frac{1}{x} )+( \frac{1}{x} )^2) \\ 5=(4)(x^2+1+( \frac{1}{x} )^2) \\ \frac{5}{4}=1+x^2+ \frac{1}{x^2} \\ \frac{5}{4}-1=x^2+ \frac{1}{x^2} \\ \\ \boxed{ \frac{1}{4}=x^2+ \frac{1}{x^2} }$

Saludos!