Question

Знайдіть значення виразу

Answer 1

Объяснение:

$\sqrt[3]{5-2\sqrt{6} }*\sqrt[6]{49+20\sqrt{6} }= 1. \\\sqrt[6]{49+20\sqrt{6} }=\sqrt[6]{25+20\sqrt{6}+24 } =\sqrt[6]{5^2+2*5*2\sqrt{6}+(\sqrt{24})^2 } } = \\=\sqrt[6]{5^2+2*5*\sqrt{24} +(\sqrt{24})^2 } =\sqrt[6]{(5+\sqrt{24} )^2}=\sqrt[3]{|5+2\sqrt{6}| } =\sqrt[3]{5+2\sqrt{6} }.\\ \sqrt[3]{5-2\sqrt{6} } *\sqrt[3]{5+2\sqrt{6} }=\sqrt[3]{(5-2\sqrt{6})*(5+2\sqrt{6}) }=\sqrt[3]{5^2-(2\sqrt{6})^2 }=\\ =\sqrt[3]{26-4*6} =\sqrt[3]{25-24}=\sqrt[3]{1} =1.$