a) \(A=4x^2-x+9\)
\(\Leftrightarrow A=4x^2-x+\dfrac{1}{16}+\dfrac{143}{16}\)
\(\Leftrightarrow A=\left(4x^2-x+\dfrac{1}{16}\right)+\dfrac{143}{16}\)
\(\Leftrightarrow A=4\left(x^2-\dfrac{1}{4}x+\dfrac{1}{64}\right)+\dfrac{143}{16}\)
\(\Leftrightarrow A=4\left[x^2-2.x.\dfrac{1}{8}+\left(\dfrac{1}{8}\right)^2\right]+\dfrac{143}{16}\)
\(\Leftrightarrow A=4\left(x-\dfrac{1}{8}\right)^2+\dfrac{143}{16}\)
Vậy GTNN của \(A=\dfrac{143}{16}\) khi \(x-\dfrac{1}{8}=0\Leftrightarrow x=\dfrac{1}{8}\)
b) \(A=x^2-5x+4\)
\(\Leftrightarrow A=x^2-5x+\dfrac{25}{4}-\dfrac{9}{4}\)
\(\Leftrightarrow A=\left(x^2-5x+\dfrac{25}{4}\right)-\dfrac{9}{4}\)
\(\Leftrightarrow A=\left[x^2-2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2\right]-\dfrac{9}{4}\)
\(\Leftrightarrow A=\left(x-\dfrac{5}{2}\right)^2-\dfrac{9}{4}\)
Vậy GTNN của \(A=\dfrac{-9}{4}\) khi \(x-\dfrac{5}{2}=0\Leftrightarrow x=\dfrac{5}{2}\)
