Question

Tính : ( 1 - \(\sqrt[3]{3}\))\(^3\) + ( 1 + \(\sqrt[3]{3})^3\)

Answer 1

\(\left(1-\sqrt[3]{3}\right)^3+\left(1+\sqrt[3]{3}\right)^3\)

\(=\left(1-\sqrt[3]{3}+1+\sqrt[3]{3}\right)\cdot\left[\left(1-\sqrt[3]{3}\right)^2-\left(1-\sqrt[3]{3}\right)\cdot\left(1+\sqrt[3]{3}\right)+\left(1+\sqrt[3]{3}\right)^2\right]\)\(=1\cdot\left(1-2\sqrt[3]{3}+\left(\sqrt[3]{3}\right)^2-1+\left(\sqrt[3]{3}\right)^2+1+2\sqrt[3]{3}+\left(\sqrt[3]{3}\right)^2\right)\)

\(=1+2\cdot\sqrt[3]{9}\)