Ta thấy: \(\left\{\begin{matrix}\left(2x+\frac{1}{4}\right)^4\ge0\\\left|y+\frac{11}{3}\right|\ge0\end{matrix}\right.\)
\(\Rightarrow\left(2x+\frac{1}{4}\right)^4+\left|y+\frac{11}{3}\right|\ge0\)
\(\Rightarrow\left(2x+\frac{1}{4}\right)^4+\left|y+\frac{11}{3}\right|-1\ge-1\)
\(\Rightarrow A\ge-1\)
Dấu "=" xảy ra khi \(\left\{\begin{matrix}\left(2x+\frac{1}{4}\right)^4=0\\\left|y+\frac{11}{3}\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}2x+\frac{1}{4}=0\\y+\frac{11}{3}=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=-\frac{1}{8}\\y=-\frac{11}{3}\end{matrix}\right.\)
Vậy \(Min_A=-1\) khi \(\left\{\begin{matrix}x=-\frac{1}{8}\\y=-\frac{11}{3}\end{matrix}\right.\)
