gtnn A = 2(x2 +6x/4 + 9/16) - 9/8 +4
=> Amin = 4 - 9/8 = 23/8
( bn hiu dc cx là giỏi lắm r)
\(A=2x^2+3x+4\)
\(=\left(\sqrt{2}x\right)^2+2.\sqrt{2}x.\dfrac{3}{2\sqrt{2}}+\left(\dfrac{3}{2\sqrt{2}}\right)^2-\left(\dfrac{3}{2\sqrt{2}}\right)^2+4\)
\(=\left(\sqrt{2}x+\dfrac{9}{8}\right)^2+\dfrac{23}{8}\)
Ta có : \(\left(\sqrt{2}x+\dfrac{9}{8}\right)^2\ge0\Rightarrow\left(\sqrt{2}x+\dfrac{9}{8}\right)+\dfrac{23}{8}\ge\dfrac{23}{8}\)
\(\Rightarrow A\ge\dfrac{23}{8}\)
Dấu = xảy ra \(\Leftrightarrow\left(\sqrt{2}x+\dfrac{9}{8}\right)^2=0\Rightarrow\sqrt{2}x+\dfrac{9}{8}=0\Rightarrow\sqrt{2}x=-\dfrac{9}{8}\Rightarrow x=\dfrac{-9\sqrt{2}}{16}\)
Vậy MinA = \(\dfrac{23}{8}\) khi x = \(\dfrac{9\sqrt{2}}{16}\)
