A) \[\frac{1}{\sqrt{3}}\]
B) \[2\sqrt{3}\]
C) \[\sqrt{3}\]
D) 2
Correct Answer: C
Solution :
\[x=\frac{\sqrt{3}}{2}\] Let, \[z=\sqrt{1+x}+\sqrt{1-x}\] \[{{z}^{2}}=1+x+1-x+2\sqrt{1-{{x}^{2}}}\] \[{{z}^{2}}=2+2\sqrt{1-\frac{3}{4}}\] \[=\,\,\,2+2\times \frac{1}{2}\] \[{{z}^{2}}=3\Rightarrow z=\underline{\sqrt{\mathbf{3}}}\]
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