a) \(x^2+10x+28=\left(x^2+10x+25\right)+3=\left(x+5\right)^2+3\ge3\)
Dấu "=" xảy ra \(\Leftrightarrow x=-5\)
b) \(4x^2-4x+\dfrac{7}{2}=\left(4x^2-4x+1\right)+\dfrac{5}{2}=\left(2x-1\right)^2+\dfrac{5}{2}\ge\dfrac{5}{2}\)
Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{2}\)
c) \(2x+5x^2=5\left(x^2+\dfrac{2}{5}x+\dfrac{1}{25}\right)-\dfrac{1}{5}=5\left(x+\dfrac{1}{5}\right)^2-\dfrac{1}{5}\ge-\dfrac{1}{5}\)
Dấu "=" xảy ra \(\Leftrightarrow x=-\dfrac{1}{5}\)
d) \(3\left(x^2-\dfrac{2}{3}x+\dfrac{1}{9}\right)+\dfrac{2}{3}=3\left(x-\dfrac{1}{3}\right)^2+\dfrac{2}{3}\ge\dfrac{2}{3}\)
Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{3}\)
