If $$x = 3 + \sqrt 8 {\text{,}}$$   then $${x^2} + \frac{1}{{{x^2}}}$$   is equal to?

A. 38

B. 36

C. 34

D. 30

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \Rightarrow x = 3 + \sqrt 8 \cr & \Rightarrow {x^2} = 9 + 8 + 2 \times 3\sqrt 8 \cr & \Rightarrow {x^2} = 17 + 6\sqrt 8 \cr & \Rightarrow \frac{1}{{{x^2}}} = 17 - 6\sqrt 8 \cr & \therefore {x^2} + \frac{1}{{{x^2}}} \cr & = 17 + 6\sqrt 8 + 17 - 6\sqrt 8 \cr & = 34 \cr} $$