Đáp án:
m=418
Giải thích các bước giải:
\(\begin{array}{l}
Xét:\Delta \ge 0\\
\to 9 - 4\left( { - m} \right) \ge 0\\
\to 9 + 4m \ge 0\\
\to m \ge - \dfrac{9}{4}\\
\to \left[ \begin{array}{l}
x = \dfrac{{ - 3 + \sqrt {4m + 9} }}{2}\\
x = \dfrac{{ - 3 - \sqrt {4m + 9} }}{2}
\end{array} \right.\\
Vi - et:\left\{ \begin{array}{l}
{x_1} + {x_2} = - 3\\
{x_1}{x_2} = - m
\end{array} \right.\\
Co:2{x_1} + 3{x_2} = 13\\
\to 2\left( {{x_1} + {x_2}} \right) + {x_2} = 13\\
\to \left[ \begin{array}{l}
2.\left( { - 3} \right) + \dfrac{{ - 3 + \sqrt {4m + 9} }}{2} = 13\\
2.\left( { - 3} \right) + \dfrac{{ - 3 - \sqrt {4m + 9} }}{2} = 13
\end{array} \right.\\
\to \left[ \begin{array}{l}
- 12 - 3 + \sqrt {4m + 9} = 26\\
- 12 - 3 - \sqrt {4m + 9} = 26
\end{array} \right.\\
\to \left[ \begin{array}{l}
\sqrt {4m + 9} = 41\\
\sqrt {4m + 9} = - 41\left( l \right)
\end{array} \right.\\
\to 4m + 9 = 1681\\
\to m = 418
\end{array}\)
