a/ \(\Delta'=\left(m-1\right)^2-\left(m+1\right)=m^2-3m>0\Rightarrow\left[{}\begin{matrix}m< 0\\m>3\end{matrix}\right.\)
b/ Theo Viet ta có: \(\left\{{}\begin{matrix}x_1+x_2=2\left(m-1\right)\\x_1x_2=m+1\end{matrix}\right.\)
Kết hợp điều kiện đề bài ta có hệ:
\(\left\{{}\begin{matrix}x_1+x_2=2\left(m-1\right)\\x_1=3x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}3x_2+x_2=2\left(m-1\right)\\x_1=3x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_2=\frac{m-1}{2}\\x_2=\frac{3\left(m-1\right)}{2}\end{matrix}\right.\)
Mặt khác cũng theo Viet: \(x_1x_2=m+1\)
\(\Rightarrow\frac{3\left(m-1\right)}{2}.\frac{\left(m-1\right)}{2}=m+1\)
\(\Leftrightarrow3\left(m-1\right)^2=4m+4\)
\(\Leftrightarrow3m^2-10m-1=0\) \(\Rightarrow m=\frac{5\pm2\sqrt{7}}{3}\) (đều thỏa mãn)
