Question

Aratati ca numarul a=$4supra \sqrt{6} + \sqrt{2} + \sqrt{2} ( \sqrt{2} - \sqrt{3} )+2supra \sqrt{2}$

Answer 1

[tex]a=\frac{4}{\sqrt6+\sqrt2}+\sqrt2(\sqrt2-\sqrt3)+\frac{2}{\sqrt2}\\ a=\frac{4(\sqrt6-\sqrt2)}{(\sqrt6+\sqrt2)(\sqrt6-\sqrt2)}+2-\sqrt6+\frac{2\sqrt2}{2}\\ a=\frac{4(\sqrt6-\sqrt2)}{6-2}+2-\sqrt6+\sqrt2\\ a=\sqrt6-\sqrt2+2-\sqrt6+\sqrt2\\ a=2[/tex]