Đáp án: m=0 hoặc m=-32/15
Giải thích các bước giải:
$\begin{array}{l}
\Delta ' > 0\\
\Rightarrow {\left( {3m - 2} \right)^2} - 4.3.\left( { - 3m - 1} \right) > 0\\
\Rightarrow 9{m^2} - 12m + 4 + 36m + 12 > 0\\
\Rightarrow 9{m^2} + 24m + 16 > 0\\
\Rightarrow {\left( {3m} \right)^2} + 2.3m.4 + 16 > 0\\
\Rightarrow {\left( {3m + 4} \right)^2} > 0\\
\Rightarrow m \ne - \frac{4}{3}\\
Theo\,Viet:\left\{ \begin{array}{l}
{x_1} + {x_2} = \frac{{3m - 2}}{3}\\
{x_1}{x_2} = \frac{{ - 3m - 1}}{3}
\end{array} \right.\\
Do:3{x_1} - 5{x_2} = 6\\
\Rightarrow 3\left( {{x_1} + {x_2}} \right) - 8{x_2} = 6\\
\Rightarrow 3.\frac{{3m - 2}}{3} - 8{x_2} = 6\\
\Rightarrow 3m - 2 - 8{x_2} = 6\\
\Rightarrow {x_2} = \frac{{3m - 8}}{8}\\
\Rightarrow {x_1} = \frac{{3m - 2}}{3} - {x_2} = \frac{{15m + 8}}{{24}}\\
\Rightarrow {x_1}{x_2} = \frac{{3m - 8}}{8}.\frac{{15m + 8}}{{24}} = \frac{{ - 3m - 1}}{3}\\
\Rightarrow \left( {3m - 8} \right)\left( {15m + 8} \right) = 64.\left( { - 3m - 1} \right)\\
\Rightarrow 45{m^2} + 24m - 120m - 64 + 192m + 64 = 0\\
\Rightarrow 45{m^2} + 96m = 0\\
\Rightarrow m\left( {45m + 96} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
m = 0\left( {tm} \right)\\
m = \frac{{ - 32}}{{15}}\left( {tm} \right)
\end{array} \right.
\end{array}$
Vậy m=0 hoặc m=-32/15
