Đáp án:
a) m=35
Giải thích các bước giải:
\(\begin{array}{l}
Xét:\Delta ' \ge 0\\
\to 36 - m \ge 0\\
\to 36 \ge m\\
\to \left[ \begin{array}{l}
x = 6 + \sqrt {36 - m} \\
x = 6 - \sqrt {36 - m}
\end{array} \right.\\
Vi - et:\left\{ \begin{array}{l}
{x_1} + {x_2} = 12\\
{x_1}{x_2} = m
\end{array} \right.\\
a){x_1} - {x_2} = 2\\
\to {x_1}^2 - 2{x_1}{x_2} + {x_2}^2 = 4\\
\to {x_1}^2 + 2{x_1}{x_2} + {x_2}^2 - 4{x_1}{x_2} = 4\\
\to {\left( {{x_1} + {x_2}} \right)^2} - 4{x_1}{x_2} = 4\\
\to {12^2} - 4m = 4\\
\to m = 35\left( {TM} \right)\\
b){x_1} = \dfrac{3}{2}{x_2}\\
\to 2\left( {{x_1} + {x_2}} \right) = 5{x_2}\\
\to \left[ \begin{array}{l}
2.12 = 5\left( {6 + \sqrt {36 - m} } \right)\\
2.12 = 5\left( {6 - \sqrt {36 - m} } \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
5\sqrt {36 - m} = - 6\left( l \right)\\
5\sqrt {36 - m} = 6
\end{array} \right.\\
\to 25\left( {36 - m} \right) = 36\\
\to m = \dfrac{{864}}{{25}}\left( {TM} \right)
\end{array}\)
