Đáp án:
\(\left[ \begin{array}{l}
m = 19\\
m = - 29\\
m = 7\\
m = - 17\\
m = 3\\
m = - 13\\
m = 1\\
m = - 11\\
m = - 1\\
m = - 9\\
m = - 2\\
m = - 8\\
m = - 3\\
m = - 7\\
m = - 4\\
m = - 6
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \dfrac{{24m - 168}}{{{m^2} - 2m - 35}}\\
= \dfrac{{24m - 168}}{{\left( {m - 7} \right)\left( {m + 5} \right)}}\\
= \dfrac{{24\left( {m - 7} \right)}}{{\left( {m - 7} \right)\left( {m + 5} \right)}}\\
= \dfrac{{24}}{{m + 5}}\\
A \in Z \Leftrightarrow \dfrac{{24}}{{m + 5}} \in Z\\
\Leftrightarrow m + 5 \in U\left( {24} \right)\\
\to \left[ \begin{array}{l}
m + 5 = 24\\
m + 5 = - 24\\
m + 5 = 12\\
m + 5 = - 12\\
m + 5 = 8\\
m + 5 = - 8\\
m + 5 = 6\\
m + 5 = - 6\\
m + 5 = 4\\
m + 5 = - 4\\
m + 5 = 3\\
m + 5 = - 3\\
m + 5 = 2\\
m + 5 = - 2\\
m + 5 = 1\\
m + 5 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
m = 19\\
m = - 29\\
m = 7\\
m = - 17\\
m = 3\\
m = - 13\\
m = 1\\
m = - 11\\
m = - 1\\
m = - 9\\
m = - 2\\
m = - 8\\
m = - 3\\
m = - 7\\
m = - 4\\
m = - 6
\end{array} \right.
\end{array}\)
