m thỏa mãn hệ
\(\left\{{}\begin{matrix}\Delta\ge0\\2x_1-3x_2=6\end{matrix}\right.\) \(\begin{matrix}\left(1\right)\\\left(2\right)\end{matrix}\) <=> \(\left(1\right)\Leftrightarrow4-\left(m+1\right)\ge0;m\le3\) (a)
đk m pt có hai nghiệm
\(x_{1,2}=2\pm\sqrt{3-m}\) ;
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x_1=2-\sqrt{3-m}\\x_2=2+\sqrt{3-m}\end{matrix}\right.\\\left\{{}\begin{matrix}x_1=2+\sqrt{3-m}\\x_2=2-\sqrt{3-m}\end{matrix}\right.\end{matrix}\right.\) \(\begin{matrix}\left(I\right)\\\\\\\left(II\right)\end{matrix}\)
\(\left(I\right)+\left(2\right)\Leftrightarrow2\left(2-\sqrt{3-m}\right)-3\left(2+\sqrt{3-m}\right)=6\)
\(\Leftrightarrow-5\sqrt{3-m}=6-4+6=8\) vô nghiệm
\(\left(II\right)+\left(2\right)\Leftrightarrow2\left(2+\sqrt{3-m}\right)-3\left(2-\sqrt{3-m}\right)=6\)
\(\Leftrightarrow5\sqrt{3-m}=6-4+6=8\) vô nghiệm
\(\Leftrightarrow3-m=\dfrac{64}{25};m=\dfrac{11}{25}\) (b)
(a) và (b) m -11/25 nhận
