Câu trả lời:
\(A=\left(x+1\right)^2+\left(y-2\right)^2+9\)
Có: \(\left(x+1\right)^2\ge0;\left(y-2\right)^2\ge0\)
\(\left(x+1\right)^2+\left(y-2\right)^2+9\ge9\)
Dấu "=" xảy ra khi: \(\hept{\begin{cases}\left(x+1\right)^2=0\\\left(y-2\right)^2=0\end{cases}}\Rightarrow\hept{\begin{cases}x+1=0\\y-2=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-1\\y=2\end{cases}}\) .
Vậy: \(Min_A=9\) tại \(\hept{\begin{cases}x=-1\\y=2\end{cases}}\)