\(\Delta'=1-m+1=2-m\ge0\Rightarrow m\le2\)
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=-2\\x_1x_2=m-1\end{matrix}\right.\)
Để pt có 2 nghiệm là nghịch đảo nhau \(\Leftrightarrow x_1x_2=1\)
\(\Rightarrow m-1=1\Rightarrow m=2\)
\(\left\{{}\begin{matrix}y_1=x_1+\frac{1}{x_2}\\y_2=x_2+\frac{1}{x_1}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}y_1+y_2=x_1+x_2+\frac{1}{x_1}+\frac{1}{x_2}\\y_1y_2=\left(x_1+\frac{1}{x_2}\right)\left(x_2+\frac{1}{x_1}\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}y_1+y_2=x_1+x_2+\frac{x_1+x_2}{x_1x_2}\\y_1y_2=\frac{\left(x_1x_2+1\right)^2}{x_1x_2}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}y_1+y_2=-2-\frac{2}{m-1}=\frac{-2m}{m-1}\\y_1y_2=\frac{m^2}{m-1}\end{matrix}\right.\)
Theo Viet đảo, \(y_1;y_2\) là nghiệm: \(y^2+\frac{2m}{m-1}y+\frac{m^2}{m-1}=0\) (\(m\ne1\))
