Question

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

Answer 1

We know that,

$a^3-b^3=(a-b{)}^3+3ab(a-b)$

Here,

$a=x$

$b=\frac{1}{x}$

Substitute these values in the above equation.

$x^3-\frac{1}{x^3}={(x-\frac{1}{x})}^3+3(x-\frac{1}{x})$

$=(3{)}^3+3(3)$

$=27+9$

$=36$

Hence, the required answer is $36$.