Question

$\sqrt[3]{5-\sqrt{17} }$*$\sqrt[3]{5+\sqrt{17} }$

Answer 1

Ответ:

$\sqrt[3]{5-\sqrt{17}}\cdot \sqrt[3]{5+\sqrt{17}}=\sqrt[3]{(5-\sqrt{17})(5+\sqrt{17})}=\sqrt[3]{5^2-17}=\sqrt[3]{8}=\sqrt[3]{2^3}=2$

Answer 2

Ответ:

Объяснение:

$\sqrt[3]{5-\sqrt{17}} *\sqrt[3]{5+\sqrt{17}} =\\\\\sqrt[3]{(5-\sqrt{17})(5+\sqrt{17})} =\\\\\sqrt[3]{5(5+\sqrt{17})-\sqrt{17}(5+\sqrt{17}) } =\\\\\sqrt[3]{5*5+5\sqrt{17} -\sqrt{17}(5+\sqrt{17}) } =\\\\\sqrt[3]{5*5+5\sqrt{17}-\sqrt{17}*5-\sqrt{17}\sqrt{17} } =\\\\\sqrt[3]{5^2+0-\sqrt{17^2} } =\sqrt[3]{5^2-17} =\\\\\sqrt[3]{25-17} =\sqrt[3]{8} =\sqrt[3]{2^3}=\boxed{2}$