Question

ВЫЧИСЛИТЕ:
$( \sqrt[6]{6} - \sqrt[6]2} )(( \sqrt[3]{6} + \sqrt[3]{2} ) ^{2} - \sqrt[3]{12} )( \sqrt[6]{6} + \sqrt[6]{2} )=$

Answer 1

$( \sqrt[6]{6} - \sqrt[6]{2} )(( \sqrt[3]{6}+ \sqrt[3]{2} )^2- \sqrt[3]{12} )( \sqrt[6]{6} + \sqrt[6]{2} )= \\ =( \sqrt[3]{6} - \sqrt[3]{2} )((\sqrt[3]{6})^2+ (\sqrt[3]{2})^2+2\sqrt[3]{6}\cdot \sqrt[3]{2}- \sqrt[3]{12})= \\ = (\sqrt[3]{6} - \sqrt[3]{2})( \sqrt[3]{36} +2 \sqrt[3]{12} + \sqrt[3]{4} -\sqrt[3]{12})=(\sqrt[3]{6}-\sqrt[3]{2})(\sqrt[3]{36}+\sqrt[3]{12}+\sqrt[3]{4})=$$=(\sqrt[3]{6})^3-(\sqrt[3]{2})^3=6-2 = 4$