Question

$\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$ is $\frac{m}{11}$. Find $m$

Answer 1

$\frac{4+\sqrt{5}}{4-\sqrt{5}}-\frac{4-\sqrt{5}}{4+\sqrt{5}}=\frac{(4+\sqrt{5}{)}^2+(4-\sqrt{5}{)}^2}{16-5}$

$=\frac{16+8\sqrt{5}+5+16-8\sqrt{5}+5}{11}$

$=\frac{42}{11}=\frac{m}{11}$

$\therefore m=42$