Question

Даю 30 баллов
Решение нужно написанное и желательно подробно ​.Флуд в бан

Answer 1

$\sqrt[4]{6} *\frac{\sqrt{14\sqrt{6}-24}-\sqrt{5\sqrt{6}-12}}{3\sqrt{2}} =\sqrt[4]{6}*\frac{\sqrt{2\sqrt{6}(7-2\sqrt{6})}-\sqrt{\sqrt{6}(5-2\sqrt{6})}}{3\sqrt{2}}=\\\\=\sqrt[4]{6} *\frac{\sqrt{2\sqrt{6}(6-2\sqrt{6}+1)}-\sqrt{\sqrt{6}(3-2\sqrt{6} +2)}}{3\sqrt{2}}=\sqrt[4]{6}*\frac{\sqrt{2\sqrt{6}(\sqrt{6}-1)^{2}}-\sqrt{\sqrt{6}(\sqrt{3}-\sqrt{2})^{2}}}{3\sqrt{2}}=\\\\=\sqrt[4]{6}*\frac{\sqrt[4]{6}*[\sqrt{2}*(\sqrt{6}-1)-(\sqrt{3}-\sqrt{2}]}{3\sqrt{2}} =$

$=\frac{\sqrt[4]{6^{2}}*(2\sqrt{3}-\sqrt{2}-\sqrt{3}+\sqrt{2})}{3\sqrt{2}}=\frac{\sqrt{6}*\sqrt{3}}{3\sqrt{2}}=\frac{\sqrt{18}}{\sqrt{18}}=\boxed1$