Question

thực hiện phép tính a = \(\left(\sqrt[3]{2}+1\right)\sqrt[3]{\frac{\sqrt[3]{2}-1}{3}}\)

Answer 1

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

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

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