\(\Leftrightarrow mx^2+2x=2mx-m\)
\(\Leftrightarrow mx^2-2\left(m-1\right)x+m=0\)
Pt có 2 nghiệm khi: \(\left\{{}\begin{matrix}m\ne0\\\left(m-1\right)^2-m^2\ge0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}m\ne0\\m\le\dfrac{1}{2}\end{matrix}\right.\)
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{2\left(m-1\right)}{m}\\x_1x_2=1\end{matrix}\right.\)
\(\left(\dfrac{x_1}{x_2}\right)^2+\left(\dfrac{x_2}{x_1}\right)^2\ge2\sqrt{\dfrac{x_1x_2}{x_1x_2}}=2\)
\(\Rightarrow\left(\dfrac{x_1}{x_2}\right)^2+\left(\dfrac{x_1}{x_2}\right)^2\le2\) khi và chỉ khi \(\dfrac{x_1}{x_2}=\dfrac{x_2}{x_1}=1\)
\(\Rightarrow x_1=x_2\Rightarrow\Delta=0\Rightarrow m=\dfrac{1}{2}\)
