\[\begin{array}{l}
Phuong\,\,trinh\,\,hoanh\,\,do\,\,giao\,\,diem\,\,cua\,\,hai\,\,dths\,\,la:\\
2{x^2} + 2mx + m - 1 = - x - 1\\
\Leftrightarrow 2{x^2} + \left( {2m + 1} \right)x + m = 0\,\,\,\left( * \right)\\
So\,\,giao\,\,diem\,\,\,cua\,\,\,hai\,\,dths\,\,la\,\,so\,\,nghiem\,\,\,cua\,\,\,pt\,\,\,\left( * \right)\\
co\,\,\,\Delta = {\left( {2m + 1} \right)^2} - 2m = 4{m^2} + 4m + 1 - 2m\\
= 4{m^2} + 2m + 1 = {m^2} + 2m + 1 + 3{m^2} = {\left( {m + 1} \right)^2} + 3{m^2} > 0\,\,\forall m.\\
\Rightarrow \left( * \right)\,\,\,co\,\,\,2\,\,\,nghiem\,\,\,pb\,\,voi\,\,moi\,\,m.
\end{array}\]
