Question

For $x=2\sqrt{3}+2\sqrt{2},$ if $\frac{1}{x}$ is $\frac{\sqrt{3}-\sqrt{2}}{m}$ then $m$ is :

Answer 1

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

Rationalising the denominator, we get

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

Hence, $m=2$.