\(m\ne3\)
Gọi A, B lần lượt là giao điểm của d với Ox, Oy
\(y_A=0\Rightarrow0=\left(m-3\right)x_A+m+1\Rightarrow x_A=\frac{m+1}{3-m}\Rightarrow A\left(\frac{m+1}{3-m};0\right)\)
\(x_B=0\Rightarrow y_B=m+1\Rightarrow B\left(0;m+1\right)\)
\(S_{OAB}=\frac{1}{2}OA.OB=\frac{1}{2}.\left|x_A\right|.\left|y_B\right|=\frac{1}{2}\left|\frac{m+1}{3-m}\right|.\left|m+1\right|=\frac{\left(m+1\right)^2}{\left|6-2m\right|}\)
\(S_{OAB}=1\Rightarrow\frac{\left(m+1\right)^2}{\left|6-2m\right|}=1\Rightarrow\left[{}\begin{matrix}\frac{\left(m+1\right)^2}{6-2m}=1\\\frac{\left(m+1\right)^2}{6-2m}=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(m+1\right)^2=6-2m\\\left(m+1\right)^2=2m-6\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}m^2+4m-5=0\\m^2+7=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m=1\\m=-5\end{matrix}\right.\)
