SSC CGL 2023 PYQ — Question 72

The correct answer is option 4 i.e. -3√5.

  $x^2 + \frac{1}{x^2}$= 7

Add 2 on both sides

⇒ $x^2 + \frac{1}{x^2}$+ 2 = 7 + 2

 ⇒ (x + 1/x)² = 9

 ⇒ (x + 1/x) = 3............1

  $x^2 + \frac{1}{x^2}$= 7

Subtract 2 on both sides

 ⇒  $x^2 + \frac{1}{x^2}$- 2 = 7 - 2

 ⇒ (x - 1/x)² = 5

 ⇒ (x - 1/x) = √5 (We have given 0 < x < 1 So, 1/x > x)

 ⇒ (x - 1/x) = -√5............2

Multiplying equation 1 and 2

(x + 1/x)(x - 1/x) = -3√5

 ⇒ $x^2 - \frac{1}{x^2}$ = -3√5