Đáp án: x=9
Giải thích các bước giải:
$\begin{array}{l}
x\left( {C_x^3 + 7C_x^2} \right) = C_x^2.C_x^3\left( {x \ge 3} \right)\\
\Rightarrow x.\left( {\frac{{x!}}{{\left( {x - 3} \right)!.3!}} + 7.\frac{{x!}}{{\left( {x - 2} \right)!.2!}}} \right) = \frac{{x!}}{{\left( {x - 2} \right)!.2!}}.\frac{{x!}}{{\left( {x - 3} \right)!.3!}}\\
\Rightarrow x.\left( {\frac{{x\left( {x - 1} \right)\left( {x - 2} \right)}}{6} + 7.\frac{{x\left( {x - 1} \right)}}{2}} \right) = \frac{{x\left( {x - 1} \right)}}{2}.\frac{{x\left( {x - 1} \right)\left( {x - 2} \right)}}{6}\\
\Rightarrow x.x\left( {x - 1} \right).\left( {\frac{{x - 2}}{6} + \frac{7}{2}} \right) = x.x.\left( {x - 1} \right).\frac{{\left( {x - 1} \right)\left( {x - 2} \right)}}{{12}}\\
\Rightarrow \frac{{x - 2}}{6} + \frac{7}{2} = \frac{{\left( {x - 1} \right)\left( {x - 2} \right)}}{{12}}\left( {do\,x \ge 3} \right)\\
\Rightarrow 2x - 4 + 42 = {x^2} - 3x + 2\\
\Rightarrow {x^2} - 5x - 36 = 0\\
\Rightarrow x = 9
\end{array}$
