A) \( \Large \left(2 - \sqrt{3}\right) \) |
B) \( \Large \left(2 + \sqrt{3}\right) \) |
C) \( \Large \frac{\sqrt{3}}2{} \) |
D) \( \Large \sqrt{3} \) |
D) \( \Large \sqrt{3} \) |
\( \Large \left(\sqrt{1+a} + \sqrt{1-a}\right)^{2} \)
= \( \Large \left(1 + a\right) + \left(1 - a\right) + 2\sqrt{1-a^{2}} \)
=\( \Large 2 \left(1 + \sqrt{1 - \frac{3}{4}}\right) \)
= \( \Large 2 \left(1 + \frac{1}{2}\right) = 2 \times \frac{3}{2} = 3 \)
Therefore, \( \Large \left(\sqrt{1+a} + \sqrt{1-a}\right) = \sqrt{3} \)