Solution of this equations.....

Given, x = 2 + √3

So, x² = (2 + √3)² = 4 + 3 + 4√3 = 7 + 4√3

Now,

$\frac{1}{x} = \frac{1}{2 + \sqrt{3}} = \frac{1}{2 + \sqrt{3}} � \frac{2 - \sqrt{3}}{2 - \sqrt{3}} = \frac{2 - \sqrt{3}}{4 - 3} = 2 - \sqrt{3}$

So, ${(\frac{1}{x})}^{2} = (2 - \sqrt{3})^{2} = 4 + 3 - 4 \sqrt{3} = 7 - 4 \sqrt{3}$

Therefore, $x^{2} + \frac{1}{x^{2}} = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} = 14$