Question

If $x-\frac{1}{x}=7$, find the value of $x^3-\frac{1}{x^3}$

Answer 1

$x-\frac{1}{x}=7$
Cubing both sides,
${(x-\frac{1}{x})}^3=(7{)}^3$
$\Rightarrow x^3-\frac{1}{x^3}-3(x-\frac{1}{x})=343$
$\Rightarrow x^3-\frac{1}{x^3}-3\times 7=343$
$\Rightarrow x^3-\frac{1}{x^3}-21=343$
$\Rightarrow x^3-\frac{1}{x^3}=343+21=364$