a/ Vỡi mọi x ta có :

\(\left|x-3\right|\ge0\)

\(\Leftrightarrow\left|x-3\right|+50\ge50\)

\(\Leftrightarrow A\ge50\)

Dấu "=" xảy ra khi :

\(\left|x-3\right|=0\)

\(\Leftrightarrow x=3\)

Vậy \(A_{Min}=50\Leftrightarrow x=3\)

b/ Với mọi x ta có :

\(\left|x+8\right|\ge0\)

\(\Leftrightarrow2014-\left|x+8\right|\le2014\)

\(\Leftrightarrow B\le2014\)

Dấu "=" xảy ra khi :

\(\left|x+8\right|=0\)

\(\Leftrightarrow x=-8\)

Vậy \(B_{Max}=2014\Leftrightarrow x=-8\)

c, Với mọi x,y ta có :

\(\left\{{}\begin{matrix}\left|x-100\right|\ge0\\\left|y+2014\right|\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left|x-100\right|+\left|y+2014\right|\ge0\)

\(\Leftrightarrow\left|x-100\right|+\left|y+2014\right|-2015\ge-2015\)

\(\Leftrightarrow C\ge-2015\)

Dấu "=" xảy ra khi :

\(\left\{{}\begin{matrix}\left|x-100\right|=0\\\left|y+2014\right|=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=100\\y=-2014\end{matrix}\right.\)

Vậy \(C_{Min}=-2015\Leftrightarrow\left\{{}\begin{matrix}x=100\\y=-2014\end{matrix}\right.\)