Đáp án:
\(m = - \dfrac{{2383}}{{36}}\)
Giải thích các bước giải:
Để phương trình có 2 nghiệm phân biệt
\(\begin{array}{l}
\to \Delta > 0\\
\to 9 - 4\left( {m - 1} \right) > 0\\
\to \dfrac{9}{4} > m - 1\\
\to \dfrac{{13}}{4} > m\\
Vi - et:\left\{ \begin{array}{l}
{x_1} + {x_2} = 3\\
{x_1}{x_2} = m - 1
\end{array} \right.\\
Có:{x_1}^2 - {x_2}^2 = 50\\
\to \left( {{x_1} - {x_2}} \right)\left( {{x_1} + {x_2}} \right) = 50\\
\to 3\left( {{x_1} - {x_2}} \right) = 50\\
\to {x_1} - {x_2} = \dfrac{{50}}{3}\\
\to {x_1}^2 - 2{x_1}{x_2} + {x_2}^2 = \dfrac{{2500}}{9}\\
\to {x_1}^2 + 2{x_1}{x_2} + {x_2}^2 - 4{x_1}{x_2} = \dfrac{{2500}}{9}\\
\to {\left( {{x_1} + {x_2}} \right)^2} - 4{x_1}{x_2} = \dfrac{{2500}}{9}\\
\to 9 - 4\left( {m - 1} \right) = \dfrac{{2500}}{9}\\
\to 4\left( {m - 1} \right) = - \dfrac{{2419}}{9}\\
\to m - 1 = - \dfrac{{2419}}{{36}}\\
\to m = - \dfrac{{2383}}{{36}}
\end{array}\)
