SSC CGL 2021 PYQ — Question 65

The correct answer is option 1 i.e. $\frac{24\sqrt{2}}{5}$

⇒ $x^2-5\sqrt{2}x+1=0$

On dividing LHS and RHS by x we get,

⇒ x + 1/x = 5$\sqrt2$.

On squaring both sides we get,

x² + 1/x² = 50 - 2 = 48.

⇒ $\frac{x^3+\frac{1}{x}}{x^2+1}$

On dividing by x we get,

 ⇒ $\frac{x^2+\frac{1}{x^2}}{x+\frac{1}{x}}$ = 48/ 5$\sqrt2$

On rationalization we get,

=   $\frac{24\sqrt{2}}{5}$.