SSC CGL 2025 PYQ — Question 60

The correct answer is option 1 i.e. $\frac{12}{5}$.

$\frac{\sqrt{3+x} + \sqrt{3-x}}{\sqrt{3+x} - \sqrt{3-x}} = 2$

Let $a = \sqrt{3+x}$, and $b = \sqrt{3-x}$

$\frac{a + b}{a - b} = 2$

⇒ a + b = 2(a - b) = 2a - 2b

⇒ a = 3b

Substitute back: $\sqrt{3+x} = 3\sqrt{3-x}$

⇒ $(\sqrt{3+x})^2 = \left(3\sqrt{3-x}\right)^2$

⇒ 3 + x = 9(3 - x) = 27 - 9x

⇒ 10x = 24

⇒ x = 24/10 = 12/5