SSC CGL 2023 PYQ — Question 57

The correct answer is option 1 i.e. $24\sqrt{2}$.

Given that, $\left(x^2 + \frac{1}{x^2}\right)=6$

Squarying the given equation,

⇒ $(x^2 + {1\over x^2})^2$ = 36

⇒ $x^4 + {1\over x^4} + 2$ = 36

⇒ $x^4 + {1\over x^4}$ = 34

Again squarying both sides of the equation,

⇒ $(x^4 + {1\over x^4})^2$ = 1156

⇒ $x^8 + {1 \over x^8} + 2$ = 1156

⇒ $x^8 + { 1\over x^8}$ = 1154

Subtracting 2 from both sides of the equation,

⇒ $x^8 + { 1\over x^8} - 2$ = 1152

⇒ $(x^4 - \frac{1}{x^4})^2$ = 1152

⇒ $x^4 - \frac{1}{x^4}$ = $24\sqrt{2}$

Hence the required answer is $24\sqrt{2}$.