Question

Find $x^2,\text{if}x=\frac{\sqrt{\sqrt{6}+2}+\sqrt{\sqrt{6}+2}}{\sqrt{\sqrt{6}+\sqrt{2}}}$

Answer 1

$\frac{\sqrt{\sqrt{6}+2}+\sqrt{\sqrt{6}+2}}{\sqrt{\sqrt{6}+2}}\Rightarrow \frac{2\sqrt{\sqrt{6}+2}\sqrt{\sqrt{6}-2}}{\sqrt{\sqrt{6}+2}\sqrt{\sqrt{6}-2}}\Rightarrow \frac{2\sqrt{\sqrt{6}-12+2\sqrt{6}-2\sqrt{2}}}{\sqrt{6-2}}\Rightarrow \sqrt{6-2\sqrt{3}-2\sqrt{2}+2\sqrt{8}}\Rightarrow 6-2\sqrt{3}-2\sqrt{2}+2\sqrt{6}$