\(\begin{array}{l}
{\left( {x\sqrt x - \dfrac{2}{{{x^2}}}} \right)^{10}} = \sum\limits_{k = 0}^{10} {C_{10}^k{{\left( {x\sqrt x } \right)}^{10 - k}}{{\left( { - 1} \right)}^k}.{{\left( {\dfrac{2}{{{x^2}}}} \right)}^k}} \\
= \sum\limits_{k = 0}^{10} {C_{10}^k.{x^{10 - k}}.{{\left( {\sqrt x } \right)}^{10 - k}}{{\left( { - 1} \right)}^k}{{.2}^k}.\dfrac{1}{{{x^{2k}}}}} \\
= \sum\limits_{k = 0}^{10} {C_{10}^k.{{\left( { - 1} \right)}^k}{{.2}^k}.{x^{10 - 3k}}.{x^{\dfrac{{10 - k}}{2}}}} \\
= \sum\limits_{k = 0}^{10} {C_{10}^k.{{\left( { - 1} \right)}^k}{{.2}^k}.{x^{\dfrac{{30 - 7k}}{2}}}} \\
\Rightarrow \dfrac{{30 - 7k}}{2} = \dfrac{{10}}{3} \Rightarrow k = \dfrac{{10}}{3}\left( {KTM} \right)
\end{array}\)
Không có số hạng chứa \({x^{\dfrac{{10}}{3}}}\) trong khai triển
