Đáp án: $m = 0;m = - 4$
Giải thích các bước giải:
$\begin{array}{l}
\left| {{x_1}} \right| + \left| {{x_2}} \right| = 5\\
\Leftrightarrow {\left( {\left| {{x_1}} \right| + \left| {{x_2}} \right|} \right)^2} = 25\\
\Leftrightarrow x_1^2 + x_2^2 + 2\left| {{x_1}{x_2}} \right| = 25\\
\Leftrightarrow {\left( {{x_1} + {x_2}} \right)^2} - 2{x_1}{x_2} + 2\left| {{x_1}{x_2}} \right| = 25\\
\Leftrightarrow {\left( {2m + 3} \right)^2} - 2\left( { - 2m - 4} \right) + 2\left| { - 2m - 4} \right| = 25\\
\Leftrightarrow 4{m^2} + 12m + 9 + 4m + 8 + 4\left| {m + 2} \right| = 25\\
\Leftrightarrow 4{m^2} + 16m - 8 + 4\left| {m + 2} \right| = 0\\
\Leftrightarrow {m^2} + 4m - 2 + \left| {m + 2} \right| = 0\\
\Leftrightarrow \left| {m + 2} \right| = - {m^2} - 4m + 2\left( 1 \right)\\
Dk: - {m^2} - 4m + 2 \ge 0\\
\Leftrightarrow {m^2} + 4m + 4 \le 6\\
\Leftrightarrow {\left( {m + 2} \right)^2} \le 6\\
\Leftrightarrow - \sqrt 6 - 2 \le m \le \sqrt 6 - 2\\
\left( 1 \right) \Leftrightarrow \left[ \begin{array}{l}
- {m^2} - 4m + 2 = m + 2\\
- {m^2} - 4m + 2 = - m - 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
{m^2} + 5m = 0\\
{m^2} + 3m - 4 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
m = 0\\
m = - 5\\
m = 1\\
m = - 4
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
m = 0\\
m = - 4
\end{array} \right.\\
Vậy\,m = 0/m = - 4
\end{array}$
