Question

Choose the correct answer from the alternatives given :
If $x-\frac{1}{x}$ = 3, the value of $x^3-\frac{1}{x^3}$ is

• A. $32$
• B. $36$
• C. $40$
• D. $49$

Answer 1

The correct option is B $36$

$x-\frac{1}{x}=3$
Cubing both sides,
$x^3-\frac{1}{x^3}-3(x-\frac{1}{x})=27$
$x^3-\frac{1}{x^3}3\left(3\right)=27\Rightarrow x^3-\frac{1}{x^3}=27+9=36$