Question

Sendo $x +$ $\frac{1}{x}$ = 2, determine $x^{3} + \frac{1}{ x^{3} }$

Answer 1

Temos que:
$\Bigg(x+\dfrac{1}{x}\Bigg)=2$
$\Bigg(x+\dfrac{1}{x}\Bigg)^3=2^3$
$x^3+\dfrac{1}{x^3}+3x+\dfrac{3}{x}=8$
$x^3+\dfrac{1}{x^3}+3\Bigg(x+\dfrac{1}{x}\Bigg)=8$
$x^3+\dfrac{1}{x^3}+3\times 2=8$
$x^3+\dfrac{1}{x^3}=2$

Espero ter ajudado!