Đáp án:
\(\left[ \begin{array}{l}
m = \dfrac{7}{2}\\
m = - \dfrac{3}{2}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
Xét:\Delta ' \ge 0\\
\to {\left( {m - 1} \right)^2} + 4 \ge 0\left( {ld} \right)\forall m\\
Có:\left| {{x_1}} \right| + \left| {{x_2}} \right| = 5\\
\to {x_1}^2 + 2{x_1}{x_2} + {x_2}^2 = 25\\
\to {\left( {{x_1} + {x_2}} \right)^2} = 25\\
\to {\left( {2m - 2} \right)^2} = 25\\
\to 4{m^2} - 8m + 4 = 25\\
\to 4{m^2} - 8m - 21 = 0\\
\to \left[ \begin{array}{l}
m = \dfrac{7}{2}\\
m = - \dfrac{3}{2}
\end{array} \right.
\end{array}\)
