Question

[dgdsgf]

CMR số sau lá số nguyen dương

\(\sqrt[3]{20+14\sqrt{2}}-\sqrt[3]{14\sqrt{2}-20}\)

Answer 1

[Bùi Anh Tuấn]

Ta có

\(\sqrt[3]{20+14\sqrt{2}}-\sqrt[3]{14\sqrt{2}-20}\)

\(=\sqrt[3]{\left(\sqrt{2}\right)^3+3\cdot2\cdot2+3\cdot\sqrt{2}\cdot2^2+2^3}-\sqrt[3]{\left(\sqrt{2}\right)^3-3\cdot2\cdot2-3\cdot\sqrt{2}\cdot2^2-2^3}\)

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

\(=\sqrt{2}+2-\sqrt{2}+2=4\)