SSC Selection Post 2022 PYQ — Question 69

The correct answer is option 1 i.e. $10\sqrt {13}$.

$x^2 - \sqrt {13} x+ 1=0$

x² + 1 = $\sqrt13$x

Divide both sides by x

⇒ x + $1\over x$ = $\sqrt13$x

⇒ (x³ + x^-3) = (x³ + $1\over x^3$)

⇒ ($\sqrt13$)³ - 3 × $\sqrt13$ 

⇒ 13$\sqrt13$ - 3$\sqrt13$ = 10$\sqrt13$