\(ĐKXĐ:x\ge0\)
\(A=-\frac{1}{2x-3\sqrt{x}+2}\)
\(=-\frac{1}{2\left(x-\frac{3}{2}\sqrt{x}+1\right)}\)
\(=-\frac{1}{2\left(x-2.\frac{3}{4}\sqrt{x}+\frac{9}{16}-\frac{9}{16}+1\right)}\)
\(=-\frac{1}{2\left(\sqrt{x}-\frac{3}{4}\right)^2+\frac{7}{8}}\)
Ta có: \(2\left(\sqrt{x}-\frac{3}{4}\right)^2\ge0,\forall x\ge0\)
\(\Leftrightarrow2\left(\sqrt{x}-\frac{3}{4}\right)^2+\frac{7}{8}\ge\frac{7}{8}\)
\(\Leftrightarrow\frac{1}{2\left(\sqrt{x}-\frac{3}{4}\right)^2+\frac{7}{8}}\le\frac{8}{7}\)
\(\Leftrightarrow\frac{-1}{2\left(\sqrt{x}-\frac{3}{4}\right)^2+\frac{7}{8}}\ge-\frac{8}{7}\)
\(\Rightarrow Min_A=-\frac{8}{7}\) khi \(\sqrt{x}-\frac{3}{4}=0\Leftrightarrow\sqrt{x}=\frac{3}{4}\Leftrightarrow x=\frac{9}{16}\)
