Question

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

If $x+\frac{1}{x}$ is equal to $\frac{5\sqrt{3}+3\sqrt{2}}{m}$, then value of $m$ is :

Answer 1

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

and $\frac{1}{x}=\frac{1}{2\sqrt{3}+2\sqrt{2}}=\frac{(2\sqrt{3}-2\sqrt{2})}{(2\sqrt{3}-2\sqrt{2})\times (2\sqrt{3}+2\sqrt{2})}=\frac{(\sqrt{3}-\sqrt{2})}{2}$.

$x+\frac{1}{x}=2\sqrt{3}+2\sqrt{2}+\frac{\sqrt{3}-\sqrt{2}}{2}=\frac{(5\sqrt{3}+3\sqrt{2})}{2}$.

Therefore, value of $m=2$.