\(m\ne-4\)
\(\Delta=\left(2m+7\right)^2-4\left(m+4\right)\left(m+1\right)=8m+33\ge0\Rightarrow m\ge\frac{33}{8}\)
Theo định lý Viet: \(\left\{{}\begin{matrix}x_1+x_2=\frac{-2m-7}{m+4}\\x_1x_2=\frac{m+1}{m+4}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3x_1+x_2=1\\x_1+x_2=\frac{-2m-7}{m+4}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3x_1+x_2=1\\2x_1=1+\frac{2m+7}{m+4}=\frac{3m+11}{m+4}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\frac{3m+11}{2m+8}\\x_2=1-3x_1=\frac{-7m-24}{2m+8}\end{matrix}\right.\)
Thay vào ta được:
\(\left(\frac{3m+11}{2m+8}\right)\left(\frac{-7m-24}{2m+8}\right)=\frac{m+1}{m+4}\)
Bạn tự giải ra m
