Question

Evaluate: $\frac{7+3\sqrt{5}}{7-3\sqrt{5}}+\frac{7-3\sqrt{5}}{7+3\sqrt{5}}=$

Answer 1

$\frac{7+3\sqrt{5}}{7-3\sqrt{5}}+\frac{7-3\sqrt{5}}{7+3\sqrt{5}}$

$\Rightarrow \frac{(7+3\sqrt{5}{)}^2+(7-3\sqrt{5}{)}^2}{(7-3\sqrt{5})(7+3\sqrt{5})}$

$\Rightarrow \frac{49+45+42\sqrt{5}+49+45-42\sqrt{5}}{(7{)}^2-(3\sqrt{5}{)}^2}$

$\Rightarrow \frac{188}{49-45}=\frac{188}{4}=47$.