\(A=4x^2+2x+3\)
\(=\left(4x^2+2x+\dfrac{1}{4}\right)+\dfrac{11}{4}\)
\(=\left(2x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\)
Do : \(\left(2x+\dfrac{1}{2}\right)^2\ge0\Rightarrow\left(2x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\)
Vậy \(GTNN\) của \(A=\dfrac{11}{4}\) . Dấu \("="\) xảy ra khi : \(\left(2x+\dfrac{1}{2}\right)^2=0\Leftrightarrow x=-\dfrac{1}{4}\)