Đáp án:
\(\left[ \begin{array}{l}
m = 2\\
m = - 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
d:\,\,y = - x + 2m + 1\\
d \cap Ox = \left\{ A \right\} \Rightarrow A\left( {2m + 1;\,\,0} \right)\\
d \cap Oy = \left\{ B \right\} \Rightarrow B\left( {0;\,\,2m + 1} \right).\\
\Rightarrow {S_{AOB}} = \frac{{25}}{2}\\
\Leftrightarrow \frac{1}{2}OA.OB = \frac{{25}}{2}\\
\Leftrightarrow OA.OB = 25\\
\Leftrightarrow \left| {2m + 1} \right|.\left| {2m + 1} \right| = 25\\
\Leftrightarrow {\left( {2m + 1} \right)^2} = 25\\
\Leftrightarrow \left[ \begin{array}{l}
2m + 1 = 5\\
2m + 1 = - 5
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
2m = 4\\
2m = - 6
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
m = 2\\
m = - 3
\end{array} \right..
\end{array}\)
