SSC CGL Tier II - Quant - 29 Jan 2022

The correct answer is option 2 i.e. 0.27

x =  $\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}$

On squaring both sides we get,

x² = 1 + $\frac{\sqrt3}{2}$ + 1 - $\frac{\sqrt3}{2}$ + 2 × $\sqrt{(1 + \frac{\sqrt3}{2}) \times (1 - \frac{\sqrt{3}}{2})}$

x² = 2 - 1

x² = 1

x = +1 , -1

⇒ $\frac{√3-x}{√3+x}$ = $\frac{\sqrt3 -1}{\sqrt3 + 1}$

On rationalization,

⇒ (3 + 1 - 2$\sqrt3$)/(3 - 1)

⇒ 2 - $\sqrt3$

⇒ 2 - 1.73 = 0.27