Ta có: \(\left|x\right|>=0\forall x\)
=>\(\left|x\right|+2023>=2023\forall x\)
=>\(\dfrac{2022}{\left|x\right|+2023}< =\dfrac{2022}{2023}\forall x\)
=>\(A< =\dfrac{2022}{2023}\forall x\)
Dấu '=' xảy ra khi |x|=0
=>x=0
Vậy: \(A_{max}=\dfrac{2022}{2023}\) khi x=0
\(A=\dfrac{2022}{\left|x\right|+2023}\)
Ta thấy: \(\left|x\right|\ge0\forall x\)
\(\Rightarrow\left|x\right|+2023\ge2023\forall x\)
\(\Rightarrow\dfrac{1}{\left|x\right|+2023}\le\dfrac{1}{2023}\forall x\)
\(\Rightarrow A=\dfrac{2022}{\left|x\right|+2023}\le\dfrac{2022}{2023}\forall x\)
Dấu \("="\) xảy ra khi: \(x=0\)
Vậy \(Max_A=\dfrac{2022}{2023}\) khi \(x=0\).
