Question

$\frac{ \sqrt[4]{ 27} + 3}{ \sqrt[4]{3} + \sqrt[3]{3} }$
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Answer 1

Объяснение:

$\displaystyle\\\frac{\sqrt[4]{27}+3 }{\sqrt[4]{3}+\sqrt[3]{3} } =\frac{\sqrt[4]{3^3} +3}{\sqrt[4]{3} +\sqrt[3]{3} }=\frac{3^\frac{3}{4} +(\sqrt[3]{3})^3 }{3^\frac{1}{4}+3^\frac{1}{3} }=\frac{(3^\frac{1}{4})^3+(3^\frac{1}{3})^3 }{3^\frac{1}{4} +3^\frac{1}{3} } =$

=$\displaystyle\\=\frac{(3^\frac{1}{4}+3^\frac{1}{3})*(3^\frac{2}{4}-3^\frac{1}{4}*3^\frac{1}{3} +3^\frac{2}{3} ) }{3^\frac{1}{4} +3^\frac{1}{3} } =3^\frac{1}{2}-3^{\frac{1}{4}+\frac{1}{3} }+3^\frac{2}{3}=\sqrt{3}-\sqrt[12]{3^7}+\sqrt[3]{3^2}=\\\\\\ =\sqrt{3}-\sqrt[12]{2187} +\sqrt[3]{9}.$