A lớn nhất khi \(\frac{24}{2\left|x-2y\right|+3\left|2x+1\right|+6}\) lớn nhất
=> \(2\left|x-2y\right|+3\left|2x+1\right|+6\) nhỏ nhất
Ta có: \(\left\{{}\begin{matrix}\left|x-2y\right|\ge0\\\left|2x+1\right|\ge0\end{matrix}\right.\) \(\forall x,y\)=> \(\left\{{}\begin{matrix}2\left|x-2y\right|\ge0\\3\left|2x+1\right|\ge0\end{matrix}\right.\) => \(2\left|x-2y\right|+3\left|2x+1\right|+6\ge6\)
dấu ''='' xảy ra khi \(\left\{{}\begin{matrix}2x+1=0\\x-2y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\frac{1}{2}\\y=-\frac{1}{4}\end{matrix}\right.\)
=> \(max_A=-6+\frac{24}{6}=-6+4=-2\)
