\(P=1-\left|5x-2\right|-\left|3y+12\right|\)
Ta có:
\(\left\{{}\begin{matrix}\left|5x-2\right|\ge0\forall x\\\left|3y+12\right|\ge0\forall y\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}-\left|5x-2\right|\le0\forall x\\-\left|3y+12\right|\le0\forall y\end{matrix}\right.\)
\(\Rightarrow1-\left|5x-2\right|-\left|3y+12\right|\le1\)
Dấu '' = '' xảy ra khi:
\(\left\{{}\begin{matrix}\left|5x-2\right|=0\\\left|3y+12\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\frac{2}{5}\\y=-4\end{matrix}\right.\)
Vậy \(A_{max}=1\) khi \(x=\frac{2}{5};y=-4.\)
Chúc em học tốt!
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