If x = 1 + 3 2 - 1 - 3 2 , then the value of 2 - x 2 + x will be closest to:

Answer: Option D

$$\begin{array}{rl}& x=\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}\\ & x=\sqrt{\frac{2+\sqrt{3}}{2}}-\sqrt{\frac{2-\sqrt{3}}{2}}\\ & x^2=\frac{2+\sqrt{3}}{2}+\frac{2-\sqrt{3}}{2}-\frac{2}{2}\sqrt{4-3}\\ & x^2=1+1-1\\ & x^2=1\\ & x=\pm 1\\ & \text{At }x=1\\ & \frac{\sqrt{2}-x}{\sqrt{2}+x}=\frac{1.414-1}{1.414+1}=0.17\end{array}$$