Question

If $x-\frac{1}{x}$ = 9 then $x^3-\frac{1}{x^3}$ = _____________

• A. 756
• B. 729
• C. 702
• D. 740

Answer 1

The correct option is A

756

Given that $x-\frac{1}{x}$ = 9

Taking cube on both sides, we have
$(x-\frac{1}{x}{)}^3=(9{)}^3$

$\Rightarrow x^3-\frac{1}{x^3}-\left(3\right)\left(x\right)\left(\frac{1}{x}\right)(x-\frac{1}{x})=729$

$\Rightarrow x^3-\frac{1}{x^3}-\left(3\right)\left(9\right)=\left(729\right)$ ( Substituting $x-\frac{1}{x}=9$ )
$\Rightarrow x^3-\frac{1}{x^3}=729+27$
= 756