SSC CGL 2022 PYQ — Question 69

The correct answer is option 4 i.e. 322.

Formula used:

(a + b)² = a² + b² + 2ab           ---- (1)

Calculations:

⇒ $x = {\sqrt{5} -2\over \sqrt{5} +2}\times\frac{\sqrt5-2}{\sqrt5-2}$ 

⇒ $x = \frac{(\sqrt5 - 2)^2}{\sqrt5^2 - 2^2}$

⇒ x = 9 - 4√5

⇒ 1/x = 9 + 4√5

⇒ x + 1/x = 9 - 4√5 + 9 + 4√5 = 18

Using the equation (1), we get

⇒ (18)² = x² + x^-2 + 2

⇒ x² + x^-2 = 324 - 2 = 322