Question

4 Кто-нибудь может объяснить?!

Answer 1

$\frac{1}{\sqrt{2}+\sqrt{5}+\sqrt{7}}=\frac{1}{(\sqrt{2}+\sqrt{5})+\sqrt{7}}=\frac{\sqrt{2}+\sqrt{5}-\sqrt{7}}{(\sqrt{2}+\sqrt{5}+\sqrt{7})(\sqrt{2}+\sqrt{5}-\sqrt{7})}=\frac{\sqrt{2}+\sqrt{5}-\sqrt{7}}{(\sqrt{2}+\sqrt{5})^2-7}=\\\frac{\sqrt{2}+\sqrt{5}-\sqrt{7}}{2+5+2\sqrt{10}-7}=\frac{\sqrt{2}+\sqrt{5}-\sqrt{7}}{2\sqrt{10}}=\frac{(\sqrt{2}+\sqrt{5}-\sqrt{7})\sqrt{10}}{2\sqrt{10}\sqrt{10}}=\frac{(\sqrt{2}+\sqrt{5}-\sqrt{7})\sqrt{10}}{20}$