Question

If $y=\frac{\sqrt{5}+2}{\sqrt{5}-2}$, then

$y^2$ is $161+72\sqrt{m}$, then the value of $m$ is

Answer 1

We rationalize the denominator,
$y=\frac{\sqrt{5}+2}{\sqrt{5}-2}\times \frac{\sqrt{5}+2}{\sqrt{5}+2}$
$y=\frac{5+4+4\sqrt{5}}{5-4}$
$y=\frac{9+4\sqrt{5}}{1}$
$y^2=(9+4\sqrt{5})(9+4\sqrt{5})$
$=81+16\times 5+72\sqrt{5}$
$=161+72\sqrt{5}$