\(A=x^2+4x+5\\ =\left(x+2\right)^2+1\\ \left(x+2\right)^2\ge0\\ \Rightarrow\left(x+2\right)^2+1\ge1\)
\(\Rightarrow A_{min}=1\) khi \(x+2=0\Leftrightarrow x=-2\)
\(\left\{{}\begin{matrix}\left(x-2\right)^2\ge0\\\left(y-1\right)^2\ge0\end{matrix}\right.\Rightarrow\frac{7}{2}\left(x-2\right)^2\left(y-1\right)^2\ge0\Rightarrow B_{min}=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\y-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
\(C=\left|x-2003\right|+\left|x-1\right|=\left|2003-x\right|+\left|x-1\right|\ge\left|2003-x+x-1\right|=2002\left(\left|a\right|+\left|b\right|\ge\left|a+b\right|\right)\Rightarrow C_{min}=2002\Leftrightarrow\left(2003-x\right)\left(x-1\right)\ge0\Leftrightarrow2003\ge x\ge1\)
