Đáp án:
\(a = b = 5\)
Giải thích các bước giải:
\[\begin{array}{l}
\frac{a}{b} = \frac{{ - b}}{{ - 5}} = \frac{{ - 5}}{{ - a}};\,\,\,a + b \ne - 5\\
Ta\,\,\,co:\,\,\,\frac{a}{b} = \frac{{ - b}}{{ - 5}} = \frac{{ - 5}}{{ - a}} \Leftrightarrow \frac{a}{b} = \frac{b}{5} = \frac{5}{a}\\
\Leftrightarrow \left\{ \begin{array}{l}
5a = {b^2}\\
5b = {a^2}\\
ab = {5^2}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{5}\\
5b = {a^2}\\
\frac{{{b^2}}}{5}.b = {5^2}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{5}\\
5b = {a^2}\\
{b^3} = {5^3}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{5}\\
5b = {a^2}\\
b = 5
\end{array} \right. \Leftrightarrow a = b = 5.
\end{array}\]
