\(\left\{{}\begin{matrix}84+a\\132-a\end{matrix}\right.=B\left(a\right)\Leftrightarrow\left\{{}\begin{matrix}84+a⋮a\\132-a⋮a\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}84⋮a\\132⋮a\end{matrix}\right.\)
\(a_{max}\Leftrightarrow a=UCLN\left(84;132\right)\)
Xét: \(\left\{{}\begin{matrix}84=2^2.3.7\\132=2^2.3.11\end{matrix}\right.\)
\(UCLN\left(84;132\right)=2^2.3=12\)
Vậy \(a=12\)