a/ \(x\ge0\), đặt \(\sqrt{x}=a\ge0\)
\(A=\frac{2a}{a^2-a+1}\Leftrightarrow A.a^2-A.a+A-2a=0\Leftrightarrow A.a^2-\left(A+2\right)a+A=0\)
\(\Delta=\left(A+2\right)^2-4A^2=-3A^2+4A+4\ge0\Rightarrow A\le2\)
\(\Rightarrow A_{max}=2\) khi \(x=1\)
b/ \(x\ge0\)
\(B=-\left(x-2.\sqrt{x}.\frac{1}{2}+\frac{1}{4}\right)-\frac{7}{4}=-\left(\sqrt{x}-\frac{1}{2}\right)^2-\frac{7}{4}\le\frac{-7}{4}\)
\(\Rightarrow B_{max}=\frac{-7}{4}\) khi \(\sqrt{x}=\frac{1}{2}\Leftrightarrow x=\frac{1}{4}\)
c/ \(x\ge0\)
\(C=-2x+\sqrt{x}-1=-2\left(x-2.\sqrt{x}.\frac{1}{4}+\frac{1}{16}\right)-\frac{7}{8}\)
\(C=-2\left(\sqrt{x}-\frac{1}{4}\right)^2-\frac{7}{8}\le\frac{-7}{8}\)
\(\Rightarrow C_{max}=\frac{-7}{8}\) khi \(x=\frac{1}{16}\)
