Điền dấu thích hợp vào chỗ chấm: \(\sqrt[3]{{\frac{1}{{125}}}} + \sqrt[3]{{ - \frac{1}{{729}}}}......\sqrt[3]{{\frac{1}{{216}}}} + \sqrt[3]{{ - \frac{1}{{512}}}}\).
Giải thích
Đáp án đúng là: A
Ta có: \(\sqrt[3]{{\frac{1}{{125}}}} + \sqrt[3]{{ - \frac{1}{{729}}}} = - \frac{1}{5} + \left( { - \frac{1}{9}} \right) = - \frac{{14}}{{45}}\);
\(\sqrt[3]{{\frac{1}{{216}}}} + \sqrt[3]{{ - \frac{1}{{512}}}} = \frac{1}{6} - \frac{1}{5} = - \frac{1}{{30}}\).
Do \( - \frac{1}{{30}} = \frac{{ - 3}}{{90}} > \frac{{ - 28}}{{90}} = \frac{{ - 14}}{{45}}\) nên \(\sqrt[3]{{\frac{1}{{125}}}} + \sqrt[3]{{ - \frac{1}{{729}}}} > \sqrt[3]{{\frac{1}{{216}}}} + \sqrt[3]{{ - \frac{1}{{512}}}}\).