Question

Give full solution of 2 part

Answer 1

Answer:

$\displaystyle\frac1{\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21}}\\\\=\frac{1}{\sqrt2\sqrt5+\sqrt2\sqrt7+\sqrt3\sqrt5+\sqrt3\sqrt7}\\\\=\frac{1}{(\sqrt2+\sqrt3)(\sqrt5+\sqrt7)}\\\\=\frac{(\sqrt2-\sqrt3)(\sqrt5-\sqrt7)}{(\sqrt2+\sqrt3)(\sqrt2-\sqrt3)(\sqrt5+\sqrt7)(\sqrt5-\sqrt7)}\\\\=\frac{(\sqrt2-\sqrt3)(\sqrt5-\sqrt7)}{(2-3)(5-7)}\\\\=\frac{(\sqrt2-\sqrt3)(\sqrt5-\sqrt7)}{2}\\\\=\frac{\sqrt{10}-\sqrt{14}-\sqrt{15}+\sqrt{21}}{2}$