Question

If $\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}=x-y\sqrt{77}$, find the values of $x$ and $y$ ?

Answer 1

$\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}$

$\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}\times$ $\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}-\sqrt{7}}$

$\frac{11+7-2\sqrt{77}}{11-7}\frac{18}{3}-\frac{2}{3}\sqrt{77}=x-y\sqrt{77}x=6y=\frac{2}{3}$