Question

Вычислите, срочно нужно!!!

Answer 1

$\sqrt[3]{5 \sqrt{2}+7 }- \sqrt[3]{5 \sqrt{2}-7 } = \\ = \sqrt[3]{1+3 \sqrt{2}+6+2 \sqrt{2} } - \sqrt[3]{-1+3 \sqrt{2}-6+2 \sqrt{2} }= \\ = \sqrt[3]{(1+ \sqrt{2})^3 }- \sqrt[3]{(-1+ \sqrt{2})^3 }= \\ =1+ \sqrt{2}+1- \sqrt{2}= \\ =2$