A) 12 |
B) 14 |
C) 16 |
D) 8 |
B) 14 |
Given that, \( \Large a = 2 + \sqrt{3} \)
Then, \( \Large \frac{1}{a} = 2 - \sqrt{3} \) [by conjugate property]
Now, we have, \( \Large a^{2} + a^{-2} = \left(a + \frac{1}{a}\right)^{2} - 2 \)
= \( \Large \left(2 + \sqrt{3} + 2 - \sqrt{3}\right)^{2} - 2 \)
= \( \Large \left(4\right)^{2} - 2 = 16 - 2 = 14 \)