Rút gọn biểu thức: \[C = \frac{{{{\left( {{a^{\frac{1}{3}}} + {b^{\frac{1}{3}}}} \right)}^2}}}{{\sqrt[3]}}:\left( {2 + \sqrt[3]{{\frac{a}{b}}} + \sqrt[3]{{\frac{b}{a}}}} \right)\] ta được kết quả là:

Ta có:

\[\begin{array}{*{20}{l}}{C = \frac{{{{\left( {{a^{\frac{1}{3}}} + {b^{\frac{1}{3}}}} \right)}^2}}}{{\sqrt[3]}}:\left( {2 + \sqrt[3]{{\frac{a}{b}}} + \sqrt[3]{{\frac{b}{a}}}} \right) = \frac{{{{\left( {\sqrt[3]{a} + \sqrt[3]{b}} \right)}^2}}}{{\sqrt[3]}}:\left( {\frac{{2\sqrt[3] + \sqrt[3]{{{a^2}}} + \sqrt[3]{{{b^2}}}}}{{\sqrt[3]}}} \right)}\\{\,\,\,\,\, = \frac{{\sqrt[3]{{{a^2}}} + 2\sqrt[3] + \sqrt[3]{{{b^2}}}}}{{\sqrt[3]}}.\frac{{\sqrt[3]}}{{\sqrt[3]{{{a^2}}} + 2\sqrt[3] + \sqrt[3]{{{b^2}}}}} = 1.}\end{array}\]

Đáp án cần chọn là: B