If x = 3 + 2√2, then the value of $${x^2} + \frac{1}{{{x^2}}}$$  is:

A. 30

B. 36

C. 32

D. 34

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & x = 3 + 2\sqrt 2 \cr & \frac{1}{x} = 3 - 2\sqrt 2 \cr & x + \frac{1}{x} = 6 \cr & {x^2} + \frac{1}{{{x^2}}} = {\left( 6 \right)^2} - 2 \cr & {x^2} + \frac{1}{{{x^2}}} = 34 \cr} $$