SSC CGL 2025 PYQ — Question 57

The correct answer is Option 2 i.e. 6.

 

$\sqrt{x+3} + \sqrt{x-2} = 5$

⇒ $\left(\sqrt{x+3} + \sqrt{x-2}\right)^2 = 5^2$

⇒ $(x + 3) + (x – 2) + 2\sqrt{(x + 3)(x – 2)} = 25$

⇒ $2x + 1 + 2\sqrt{(x + 3)(x – 2)} = 25$

⇒ $2\sqrt{(x + 3)(x – 2)} = 24 - 2x$

⇒ $\sqrt{(x + 3)(x – 2)} = 12 - x$

⇒ (x + 3)(x – 2) = (12 – x)²

⇒ x² + x – 6 = 144 – 24x + x²

⇒ x – 6 = 144 – 24x

⇒ 25x = 150

⇒ x = 150/25 = 6