\(\Delta'=2-m>0\Rightarrow m< 2\)
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=2\\x_1x_2=m-1\end{matrix}\right.\)
a/ Kết hợp Viet và đề bài ta có:
\(\left\{{}\begin{matrix}x_1+x_2=2\\x_1=5x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}6x_2=2\\x_1=5x_2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_2=\frac{1}{3}\\x_1=\frac{5}{3}\end{matrix}\right.\)
\(x_1x_2=m-1\Rightarrow m-1=\frac{1}{3}.\frac{5}{3}=\frac{5}{9}\Rightarrow m=\frac{14}{9}\) (t/m)
b/ \(\left|x_1-x_2\right|=4\Leftrightarrow\left(x_1-x_2\right)^2=16\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-4x_1x_2=16\)
\(\Leftrightarrow4-4\left(m-1\right)=16\Rightarrow m-1=-3\Rightarrow m=-2\) (t/m)
