SSC CGL 2021 PYQ — Question 73

The correct answer is option 4 i.e. 47

$x-\frac{1}{x} = 1$

By squaring both sides,

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

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

$x^2+\frac{1}{x^2}=3$

By again squaring,

$(x^2+\frac{1}{x^2})^2=3^2$

$x^4+\frac{1}{x^4}+2=9$

$x^4+\frac{1}{x^4}=7$

By again squaring,

$(x^4+\frac{1}{x^4})^2=7^2$

$x^8+\frac{1}{x^8}+2=49$

$x^8+\frac{1}{x^8}=47$