Question

Thực hiện phép tính:

\(\dfrac{\sqrt[3]{2}}{\sqrt[3]{2}-1}\) -  \(\sqrt[3]{4}\)  - \(\sqrt[3]{2}\)

Answer 1

\(\dfrac{\sqrt[3]{2}}{\sqrt[3]{2}-1}-\sqrt[3]{4}-\sqrt[3]{2}\)

\(=\dfrac{\sqrt[3]{2}\left(\sqrt[3]{4}+\sqrt[3]{2}+1\right)}{\left(\sqrt[3]{2}-1\right)\left(\sqrt[3]{4}+\sqrt[3]{2}+1\right)}-\sqrt[3]{4}-\sqrt[3]{2}\)

\(=\dfrac{\sqrt[3]{8}+\sqrt[3]{4}+\sqrt[3]{2}}{2-1}-\sqrt[3]{4}-\sqrt[3]{2}\)

\(=2+\sqrt[3]{4}+\sqrt[3]{2}-\sqrt[3]{4}-\sqrt[3]{2}\)

\(=2\)