Tìm m nguyên để $\frac{24m-168}{m^2-2m-35}$ có giá trị nguyên
Ai giúp vs!!!
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Ai giúp vs!!!”
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:
\(\begin{array}{l} A = \dfrac{{24m – 168}}{{{m^2} – 2m – 35}}\\ = \dfrac{{24m – 168}}{{\left( {m – 7} \right)\left( {m + 5} \right)}}\\ = \dfrac{{24\left( {m – 7} \right)}}{{\left( {m – 7} \right)\left( {m + 5} \right)}}\\ = \dfrac{{24}}{{m + 5}}\\ A \in Z \Leftrightarrow \dfrac{{24}}{{m + 5}} \in Z\\ \Leftrightarrow m + 5 \in U\left( {24} \right)\\ \to \left[ \begin{array}{l} m + 5 = 24\\ m + 5 = – 24\\ m + 5 = 12\\ m + 5 = – 12\\ m + 5 = 8\\ m + 5 = – 8\\ m + 5 = 6\\ m + 5 = – 6\\ m + 5 = 4\\ m + 5 = – 4\\ m + 5 = 3\\ m + 5 = – 3\\ m + 5 = 2\\ m + 5 = – 2\\ m + 5 = 1\\ m + 5 = – 1 \end{array} \right. \to \left[ \begin{array}{l} m = 19\\ m = – 29\\ m = 7\\ m = – 17\\ m = 3\\ m = – 13\\ m = 1\\ m = – 11\\ m = – 1\\ m = – 9\\ m = – 2\\ m = – 8\\ m = – 3\\ m = – 7\\ m = – 4\\ m = – 6 \end{array} \right. \end{array}\)
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:
\(\begin{array}{l}
A = \dfrac{{24m – 168}}{{{m^2} – 2m – 35}}\\
= \dfrac{{24m – 168}}{{\left( {m – 7} \right)\left( {m + 5} \right)}}\\
= \dfrac{{24\left( {m – 7} \right)}}{{\left( {m – 7} \right)\left( {m + 5} \right)}}\\
= \dfrac{{24}}{{m + 5}}\\
A \in Z \Leftrightarrow \dfrac{{24}}{{m + 5}} \in Z\\
\Leftrightarrow m + 5 \in U\left( {24} \right)\\
\to \left[ \begin{array}{l}
m + 5 = 24\\
m + 5 = – 24\\
m + 5 = 12\\
m + 5 = – 12\\
m + 5 = 8\\
m + 5 = – 8\\
m + 5 = 6\\
m + 5 = – 6\\
m + 5 = 4\\
m + 5 = – 4\\
m + 5 = 3\\
m + 5 = – 3\\
m + 5 = 2\\
m + 5 = – 2\\
m + 5 = 1\\
m + 5 = – 1
\end{array} \right. \to \left[ \begin{array}{l}
m = 19\\
m = – 29\\
m = 7\\
m = – 17\\
m = 3\\
m = – 13\\
m = 1\\
m = – 11\\
m = – 1\\
m = – 9\\
m = – 2\\
m = – 8\\
m = – 3\\
m = – 7\\
m = – 4\\
m = – 6
\end{array} \right.
\end{array}\)