Question

Find the value of

$x^3+\frac{1}{x^3}$ if $x+\frac{1}{x}=2$

Answer 1

$\Rightarrow$ $x^3+\frac{1}{x^3}$

$={(x+\frac{1}{x})}^3-3x.\frac{1}{x}(x+\frac{1}{x})={\left(2\right)}^3-3\times 2=8-6=2$