SSC CGL 2023 PYQ — Question 53

The correct answer is option 3 i.e. $24\sqrt{2}$.

$x^2 - \frac{1}{x^2} = 4\sqrt{2}$...................1

Square on both sides

⇒ x⁴ + (1/x⁴) - 2 = 32

⇒ x⁴ + (1/x⁴) = 34

Now add 2 on both sides 

⇒ x⁴ + (1/x⁴) + 2 = 34 + 2

⇒ x⁴ + (1/x⁴) + 2 = 36

⇒ $(x^2+\frac{1}{x^2})^2 = 36$

$(x^2+\frac{1}{x^2}) = 6$......................2

Now,

$(x^2 - \frac{1}{x^2})(x^2 + \frac{1}{x^2}) = x^4 - \frac{1}{x^4}$

 ⇒ $x^4 - \frac{1}{x^4}$ = 6 × 4$\sqrt2$

 ⇒ $x^4 - \frac{1}{x^4}$ = 24$\sqrt2$