If x = 3 + 2√2, then the value of x^2 + 1/(x^2) is :

If $x = 3 + 2\sqrt{2}$,

then the value of $x^2 + \frac{1}{x^2}$ is = ?

If $x = 3 + 2\sqrt{2}$

x² = 9 + 8 + $12\sqrt{2}$ = 17 + $12\sqrt{2}$

and \(\frac{1}{x^2}\) = 17 - $12\sqrt{2}$

Now, $x^2 + \frac{1}{x^2}$ = 17 + $12\sqrt{2}$ + 17 - $12\sqrt{2}$ = 34