Bài tập 2.34 trang 79 SBT Toán 11

Ta có: 

\({\left( {1 + ax} \right)^n} = \mathop {\mathop \sum \nolimits^ }\limits_n^{k = 0} C_n^k{(ax)^k} = \mathop {\mathop \sum \nolimits^ }\limits_n^{k = 0} C_n^k{a^k}{x^k} = 1 + C_n^1ax + C_n^2{a^2}{x^2} + ...\)

Theo bài ra:

\(\begin{array}{l}
\left\{ {\begin{array}{*{20}{l}}
{C_n^1a = 24}\\
{C_n^2{a^2} = 252}
\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}
{na = 24}\\
{\frac{{n\left( {n - 1} \right){a^2}}}{2} = 252}
\end{array}} \right.\\
 \Rightarrow \left\{ {\begin{array}{*{20}{l}}
{na = 24}\\
{\left( {n - 1} \right)a = 21}
\end{array}} \right. \Rightarrow \left[ \begin{array}{l}
a = 3\\
n = 8
\end{array} \right.
\end{array}\)

-- Mod Toán 11 HỌC247