Question

Найдите значение выражения: $\frac{( \sqrt{15} -4) \sqrt{8+2 \sqrt{15} }}{ \sqrt{10} - \sqrt{6} }$

Answer 1

$\frac{(\sqrt{15}-4)\sqrt{8+2\sqrt{15}}}{\sqrt{10}-\sqrt6}=\frac{(\sqrt{15}-4)\sqrt{(\sqrt3+\sqrt5)^2}}{\sqrt2\cdot \sqrt5-\sqrt2\cdot \sqrt3}=\frac{(\sqrt{15}-4)(\sqrt3+\sqrt5)}{\sqrt2(\sqrt3-\sqrt5)}=\\\\=\frac{(\sqrt{15}-4)(\sqrt3+\sqrt5)^2}{\sqrt2\cdot \sqrt2(\sqrt3-\sqrt5)(\sqrt3+\sqrt5)}=\frac{(\sqrt{15}-4)(8+2\sqrt{15})}{2(3-5)}=\frac{(\sqrt{15}-4)\cdot 2\cdot (4+\sqrt{15})}{2(-2)}=\\\\=\frac{2\cdot (15-16)}{-4}=\frac{-1}{-2}=\frac{1}{2}$