Giải câu 2 trang 31 toán VNEN 9 tập 1.
a) $\frac{1}{1 - \sqrt[3]{5}}$ = $\frac{1 + \sqrt[3]{5} + (\sqrt[3]{5})^{2}}{(1 - \sqrt[3]{5})(1 + \sqrt[3]{5} + (\sqrt[3]{5})^{2})}$ = $\frac{1 + \sqrt[3]{5} + (\sqrt[3]{5})^{2}}{(1 - (\sqrt[3]{5})^{3}}$ = $\frac{1 + \sqrt[3]{5} + (\sqrt[3]{5})^{2}}{- 4}$.
b) $\frac{1}{ \sqrt[3]{2} + \sqrt[3]{3}}$ = $\frac{(\sqrt[3]{2})^{2} - \sqrt[3]{2}.\sqrt[3]{3} + (\sqrt[3]{3})^{2}}{(\sqrt[3]{2} + \sqrt[3]{3})((\sqrt[3]{2})^{2} - \sqrt[3]{2}.\sqrt[3]{3} + (\sqrt[3]{3})^{2})}$ = $\frac{\sqrt[3]{4} - \sqrt[3]{6} + \sqrt[3]{9}}{(\sqrt[3]{2})^{3} + (\sqrt[3]{3})^{3})}$ = $\frac{\sqrt[3]{4} - \sqrt[3]{6} + \sqrt[3]{9}}{5}$.
c) $\frac{1}{ 1 + \sqrt[3]{2} + 2\sqrt[3]{4}}$ = $\frac{1}{ 1 + \sqrt[3]{2} + 2(\sqrt[3]{2})^{2}}$