Ta có: \({\left( {1 + ax} \right)^n} = \mathop \sum \limits_{k = 0}^n C_n^k{(ax)^k} \)
\(= \mathop \sum \limits_{k = 0}^n C_n^k{a^k}{x^k} \)
\(= 1 + C_n^1ax + C_n^2{a^2}{x^2} + ...\)
Theo bài ra:
\(\left\{ \begin{array}{l}C_n^1a = 24\\C_n^2{a^2} = 252\end{array} \right. \)
\(\Rightarrow \left\{ \begin{array}{l}na = 24\\\dfrac{{n\left( {n - 1} \right){a^2}}}{2} = 252\end{array} \right. \)
\(\Rightarrow \left\{ \begin{array}{l}na = 24\\\left( {n - 1} \right)a = 21\end{array} \right.\)
\(\Rightarrow \left\{ \begin{array}{l}a = 3\\n = 8.\end{array} \right.\)
