\(\Leftrightarrow\Delta'>0\Leftrightarrow m^2-\left(m^2-4\right)=4>0\left(đúng\forall m\right)\)
\(x^2-2mx+m^2-4=0\Leftrightarrow\left(m-x-2\right)\left(m-x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=m+2\\x=m-2\end{matrix}\right.\)
\(đk\) \(thoa\) \(mãn:\dfrac{1}{x1}+\dfrac{3}{x2}=1\Leftrightarrow x1=x2\ne0\Rightarrow m\ne\pm2\)
\(với:\left[{}\begin{matrix}x1=m+2\\x2=m-2\end{matrix}\right.\)
\(\dfrac{1}{x1}+\dfrac{3}{x2}=1\Leftrightarrow3x1+x2=x1x2\Leftrightarrow3\left(m+2\right)+m-2=m^2-4\)
\(\Leftrightarrow\left[{}\begin{matrix}m=2+2\sqrt{3}\left(tm\right)\\m=2-2\sqrt{3}\left(tm\right)\end{matrix}\right.\)
\(với:\left[{}\begin{matrix}x1=m-2\\x2=m+2\end{matrix}\right.\)\(\Rightarrow3\left(m-2\right)+m+2=m^2-4\Leftrightarrow\left[{}\begin{matrix}m=4\left(tm\right)\\m=0\left(tm\right)\end{matrix}\right.\)
