Question

Solve:
$\sqrt{5}\left(1+\sqrt{5}\right)x=2\sqrt{5}+4$

Answer 1

$\sqrt{5}(1+\sqrt{5})x=2\sqrt{5}+4$

$x=\left(\frac{2\sqrt{5}+4}{\sqrt{5}(1+\sqrt{5})}\right)$

$=2\left(\frac{\sqrt{5}+2}{\sqrt{5}(\sqrt{5}+1)}\right)\left(\frac{\sqrt{5}-1}{\sqrt{5}-1}\right)$

$=2\left(\frac{5-\sqrt{5}+2\sqrt{5}-2}{5-1}\right)$

$=\left(\frac{3+\sqrt{5}}{2}\right)\left(\frac{\sqrt{5}}{\sqrt{5}}\right)$

$=\left(\frac{3\sqrt{5}+5}{10}\right)$

$=\left(\frac{5+3\sqrt{5}}{10}\right)$