SSC CGL 2022 PYQ — Question 33

The correct answer is option 1 i.e. 5.

$\frac{\sqrt{26-7\sqrt{3}}}{\sqrt{14+5\sqrt{3}}}= \frac{b+a\sqrt{3}}{11}$

On rationalization of the LHS part we get,

$\frac{\sqrt{26-7\sqrt{3}}}{\sqrt{14+5\sqrt{3}}} \times \sqrt{\frac{14-5\sqrt{3}}{14-5\sqrt{3}}}$

$\frac{\sqrt{364 - 130\sqrt{3} - 98\sqrt{3}+105}}{\sqrt{196 - 75}}$ = $\frac{b+a\sqrt{3}}{11}$

$\frac{\sqrt{469 - 228 \sqrt3}}{11} = \frac{b+a\sqrt{3}}{11}$

On squaring both sides we get,

469 - 228$\sqrt3$ = b² + 3a² + 2ab$\sqrt3$.

(19)² + 3(-6)² + 2 × 19 × (-6) = b² + 3a² + 2ab$\sqrt3$.

on comparing we get,

a = -6 and b = 19,

$\sqrt{(b-a)}$ = $\sqrt{(19-(-6)}$ = 5.