3 tháng 8 2024 lúc 22:34
a.
Do \(\left\{{}\begin{matrix}\left|x+2\right|\ge0\\\left|y-2\right|\ge0\end{matrix}\right.\) \(;\forall x;y\)
\(\Rightarrow2024-\left|x+2\right|-\left|y-2\right|\le2024\)
\(\Rightarrow A\le2024\)
Vậy \(A_{max}=2024\) khi \(\left\{{}\begin{matrix}\left|x+2\right|=0\\\left|y-2\right|=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-2\\y=2\end{matrix}\right.\)
b.
\(\left|2x+5\right|\ge0;\forall x\Rightarrow\left|2x+5\right|+2024\ge2024\)
Lại có \(2023>0\)
\(\Rightarrow\dfrac{2023}{\left|2x+5\right|+2024}\le\dfrac{2023}{2024}\)
Vậy \(B_{max}=\dfrac{2023}{2024}\) khi \(\left|2x+5\right|=0\Rightarrow x=-\dfrac{5}{2}\)
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