SSC CGL 2023 PYQ — Question 73

The correct answer is option 1 i.e. 12$\sqrt{10}$.

Given that

If (x − $\frac{1}{x}$ ) = 6, and x > 0,

Squaring both sides

⇒ x² + 1/x² - 2 = 36

Adding 4 on both sides

⇒ x² + 1/x² - 2 + 4 = 36 + 4 = 40

⇒ (x + 1/x)² = 40

⇒ x + 1/x = 2$\sqrt{10}$

Hence, the value of   (x² - $\frac{1}{x^2}$) = (x + 1/x) (x - 1/x) =  2$\sqrt{10}$ × 6 = 12$\sqrt{10}$