Đáp án:
a)n=5
b)\(
a_3 = 5760
\)
Giải thích các bước giải:
a)\(
\begin{array}{l}
A_n^2 + 4C_n^n = 24 \\
\Leftrightarrow \frac{{n!}}{{(n - 2)!}} + 4.\frac{{n!}}{{n!}} = 24 \\
\Leftrightarrow n(n - 1) + 4 = 24 \\
\Leftrightarrow n^2 - n - 20 = 0 \\
\Leftrightarrow \left[ {\begin{array}{*{20}c}
{n = 5(tm)} \\
{n = - 4(ktm)} \\
\end{array}} \right. \\
\end{array}
\)
b)\(
\begin{array}{l}
(4x - 3)^5 = \sum\limits_{k = 0}^5 {C_5^k .4^{5 - k} .x^{5 - k} ( - 3)^k = \sum\limits_{k = 0}^5 {C_5^k .4^{5 - k} ( - 3)^k .x^{5 - k} } } \\
5 - k = 3 \Leftrightarrow k = 2 \\
= > a_3 = C_5^2 .4^3 .( - 3)^2 = 5760 \\
\end{array}
\)