If X = 5 + 2$\sqrt{6}$ Find the value of X + $\frac{1}{X}$

The correct option is D. $10$

As X = 5 + 2$\sqrt{6}$

Then $\frac{1}{X}$ = $\frac{1}{5+2\sqrt{6}}$

$\frac{1}{X}$ = $\frac{1}{5+2\sqrt{6}}$$\times$$\left(\frac{5-2\sqrt{6}}{5-2\sqrt{6}}\right)$

$\frac{1}{X}$ = $\frac{5-2\sqrt{6}}{5^2-(2\sqrt{6}{)}^2}$

$\frac{1}{X}$ = $\frac{5-2\sqrt{6}}{25-24}$

$\frac{1}{X}$ = 5 - 2$\sqrt{6}$

Now X + $\frac{1}{X}$ = 5 + 2$\sqrt{6}$ + 5 - 2$\sqrt{6}$ = 10