Question

If $X=\sqrt{3}-\sqrt{2}$ then find $X^2+1/X^2$

Answer 1

$X=\sqrt{3}-\sqrt{2}⟹X^2=(\sqrt{3}-\sqrt{2}{)}^2=(\sqrt{3}{)}^2+(\sqrt{2}{)}^2-2(\sqrt{3}\left)\right(\sqrt{2})=5-2\sqrt{6}$

$\frac{1}{X^2}=\frac{1}{5-2\sqrt{6}}=\frac{5+2\sqrt{6}}{25-24}=5+2\sqrt{6}$

$X^2+\frac{1}{X^2}=5-2\sqrt{6}+5+2\sqrt{6}=10$