SSC CHSL 2021 PYQ — Question 66

The correct answer is option 4 i.e. 22$\sqrt{2}$

Given:

 x - $\frac{1}{x}=2\sqrt{2}$

Formula USed:

(a - b)³ = a³ - b³ - 3ab(a - b)

Explanation:

According to the given question,

 x - $\frac{1}{x}=2\sqrt{2}$

Taking cube on both sides, we get

( x - $\frac{1}{x})^3=(2\sqrt{2}$)³

⇒ x³ - $\frac{1}{x^3}$ - 3(1)(2$\sqrt{2}$) = 16$\sqrt{2}$

⇒ x³ - $\frac{1}{x^3}$ - 6$\sqrt{2}$ = 16$\sqrt{2}$

 ⇒ x³ - $\frac{1}{x^3}$ = 22$\sqrt{2}$

Hence the required answer is 22$\sqrt{2}$.