Ta có:
\(ab+bc=518\)
\(ab-ac=360\)
\(\Leftrightarrow bc+ac=158\)
\(\Leftrightarrow c\left(a+b\right)=2.79\)
\(\Leftrightarrow\left[{}\begin{matrix}c=79\\c=2\end{matrix}\right.\)
Nếu \(c=79\)
\(\Leftrightarrow a=b=1\) (loại)
Nếu \(c=2\)
\(\Leftrightarrow a+b=79\)\(\Rightarrow\left\{{}\begin{matrix}ab+2b=518\\ab-2a=360\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b=79\\ab+2b=518\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}a=79-b\\\left(79-b\right)b+2b-518=0\end{matrix}\right.\)
\(\Leftrightarrow-b^2+79b+2b-518=0\)
\(\Leftrightarrow\left[{}\begin{matrix}b=74\Rightarrow a=5\\b=7\Rightarrow a=72\end{matrix}\right.\)
Vậy \(\left(a;b;c\right)=\left(72;7;2\right)=\left(5;74;2\right)\)
