Đáp án:
\(3 > m > - 3;m \ne \dfrac{3}{2}\)
Giải thích các bước giải:
Để phương trình có 2 nghiệm phân biệt
\(\begin{array}{l}
\to \left\{ \begin{array}{l}
m \ne 3\\
{m^2} - \left( { - 3m + 3} \right)\left( {m - 3} \right) > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m \ne 3\\
{m^2} + 3{m^2} - 9m - 3m + 9 > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m \ne 3\\
4{m^2} - 12m + 9 > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m \ne 3\\
{\left( {2m - 3} \right)^2} > 0
\end{array} \right.\\
\to m \ne \left\{ {\dfrac{3}{2};3} \right\}\\
Do:{x_1} + {x_2} < 1\\
\to \dfrac{{2m}}{{m - 3}} < 1\\
\to \dfrac{{2m - m + 3}}{{m - 3}} < 0\\
\to \dfrac{{m + 3}}{{m - 3}} < 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
m + 3 > 0\\
m - 3 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
m + 3 < 0\\
m - 3 > 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
3 > m > - 3\\
\left\{ \begin{array}{l}
m < - 3\\
m > 3
\end{array} \right.\left( l \right)
\end{array} \right.\\
\to 3 > m > - 3;m \ne \dfrac{3}{2}
\end{array}\)
