If x = 3 + 2 2 , then the value of x^2 + 1x^2 is?

Answer: Option D

$$\begin{array}{rl}& x=3+2\sqrt{2}\\ & \Rightarrow x^2={\left(3+2\sqrt{2}\right)}^2\\ & \left(\text{Squaring both sides}\right)\\ & \Rightarrow x^2=9+8+12\sqrt{2}\\ & \Rightarrow x^2=17+12\sqrt{2}\\ & \Rightarrow \frac{1}{x^2}=\frac{1}{17+12\sqrt{2}}\times \frac{17-12\sqrt{2}}{17-12\sqrt{2}}\\ & \Rightarrow \frac{1}{x^2}=17-12\sqrt{2}\\ & \therefore x^2\text{ + }\frac{1}{x^2}\\ & =17+12\sqrt{2}+17-12\sqrt{2}\\ & =34\end{array}$$