giup voi
Mình giúp bạn nha
Ta có : \(3m+4n-mn=16\)
\(\Rightarrow m\left(3-n\right)+4n-12=4\)
\(\Rightarrow m\left(3-n\right)-4\left(3-n\right)=4\)
\(\Rightarrow\left(m-4\right)\left(3-n\right)=4\)
\(\Rightarrow\) \(\left[{}\begin{matrix}m-4\in\left\{1,2,4,-1,-2,-4\right\}\\3-n\in\left\{4,2,1,-4,-2,-1\right\}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}m\in\left\{5,6,8,3,2,0\right\}\\n\in\left\{-1,1,2,7,5,4\right\}\end{matrix}\right.\)
đoạn cuối khi tìm m,n bạn kẻ bảng cho dễ làm (trong này không có kẻ nên mình làm tạm vậy nha )
Ta có : 3m+4n-mn=16
\(\Rightarrow\) 3m+4n-mn-12 =4
\(\Rightarrow\)m (3-n)-4(3-n)=4
\(\Rightarrow\)(m-4) (3-n) =4
Ta có : 4= \(1\cdot4\) =\(4\cdot1\) =\(2\cdot2\) =\(\left(-1\right)\cdot\left(-4\right)\) =\(\left(-4\right)\cdot\left(-1\right)\)
- \(\left\{{}\begin{matrix}m-4=1\\3-n=4\end{matrix}\right.\)\(\Rightarrow\) \(\left\{{}\begin{matrix}m=5\\n=-1\end{matrix}\right.\)
-\(\left\{{}\begin{matrix}m-4=4\\3-n=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=8\\n=2\end{matrix}\right.\)
-\(\left\{{}\begin{matrix}m-4=2\\3-n=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=6\\n=1\end{matrix}\right.\)
-\(\left\{{}\begin{matrix}m-4=-1\\3-n=-4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=3\\n=7\end{matrix}\right.\)
-\(\left\{{}\begin{matrix}m-4=-4\\3-n=-1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=0\\n=4\end{matrix}\right.\)
vậy \(\left(m;n\right)\in\left[\left(5;1\right),\left(8;2\right),\left(6;1\right),\left(0;4\right)\right]\)
