\(A=3x-5x^2+7\)
\(\Rightarrow A=\left(-5x^2-3x-7\right)\)
\(\Rightarrow-\left[\left(4x^2-4x+1\right)+\left(x^2+x+\frac{1}{4}\right)-\frac{25}{4}\right]\)
\(\Rightarrow A=\frac{25}{4}-\left(2x-1\right)^2-\left(x+\frac{1}{2}\right)^2\le\frac{25}{4}\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}2x-1=0\\x+\frac{1}{2}=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}2x=1\\x=-\frac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\)
Vậy \(Max_A=\frac{25}{4}\Leftrightarrow\left\{{}\begin{matrix}x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\)
