\(\Delta=m^2-8\left(m-2\right)=\left(m-4\right)^2\ge0;\forall m\)
\(\Rightarrow\) Phương trình luôn có nghiệm với mọi m
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=\frac{m}{2}\\x_1x_2=\frac{m-2}{2}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}y_1+y_2=x_1+x_2\\y_1^2+y_2^2=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y_1+y_2=\frac{m}{2}\\\left(y_1+y_2\right)^2-2y_1y_2=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y_1+y_2=\frac{m}{2}\\y_1y_2=\frac{m^2}{8}-\frac{1}{2}\end{matrix}\right.\)
Theo Viet đảo, \(y_1;y_2\) là nghiệm:
\(y^2-\frac{m}{2}y+\frac{m^2}{8}-\frac{1}{2}=0\Leftrightarrow8y^2-4m.y+m^2-4=0\)
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