Question

\(\sqrt[3]{2+10\sqrt{\frac{1}{27}}}\) + \(\sqrt[3]{2+10\sqrt{\frac{1}{27}}}\)

E = \(\sqrt[3]{4+\frac{5}{3}\sqrt{\frac{31}{3}}}\)+ \(\sqrt[3]{4-\frac{5}{3}\sqrt{\frac{31}{3}}}\)

Answer 1

\(E=\)( ghi đề vào đây )

\(E=\sqrt[3]{4+\frac{5}{3}.\frac{\sqrt{31}}{\sqrt{3}}}+\sqrt[3]{4-\frac{5}{3}.\frac{\sqrt{31}}{3}}\)

\(E=\sqrt[3]{4+\frac{5\sqrt{31}}{3\sqrt{3}}}+\sqrt[3]{4+\frac{5.\sqrt{31}}{3\sqrt{3}}}\)

\(E\approx1\)

Answer 2

\(E^3=4+\frac{5}{3}\sqrt{\frac{31}{3}}+4-\frac{5}{3}\sqrt{\frac{31}{3}}+3\sqrt[3]{\left(16-\frac{25}{9}.\frac{31}{3}\right)}\left(\sqrt[3]{4+\frac{5}{3}\sqrt{\frac{31}{3}}}+\sqrt[3]{4-\frac{5}{3}\sqrt{\frac{31}{3}}}\right)\)

\(\Leftrightarrow E^3=8-7E\)

\(\Leftrightarrow E^3+7E-8=0\)

\(\Leftrightarrow\left(E-1\right)\left(E^2+E+8\right)=0\)

\(\Leftrightarrow E=1\)