Ta có \(2x-x^2+7=-\left(x^2-2x+1\right)+8=-\left(x+1\right)^2+8\le8\Leftrightarrow2x-x^2+7\le8\Leftrightarrow\sqrt{2x-x^2+7}\le2\sqrt{2}\Leftrightarrow2+\sqrt{2x-x^2+7}\le2+2\sqrt{2}\Leftrightarrow\frac{2018}{2+\sqrt{2x-x^2+7}}\ge\frac{2018}{2+2\sqrt{2}}=\frac{1009}{\sqrt{2}+1}=\frac{1009\left(\sqrt{2}-1\right)}{2-1}=1009\sqrt{2}-1009\)Dấu '=' xảy ra khi \(\left(x+1\right)^2=0\Leftrightarrow x=-1\)
Vậy GTNN của A là \(1009\sqrt{2}-1009\)
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