\(2x^2-2x+4=2\left(x^2-x+2\right)\)
\(=2\left(x^2-2.x.\frac{1}{2}+\frac{1}{4}+\frac{7}{4}\right)\)
\(=2\left[\left(x-\frac{1}{2}\right)^2+\frac{7}{4}\right]\)
\(=2\left(x-\frac{1}{2}\right)^2+\frac{7}{2}\ge\frac{7}{2}\)
Vậy GTNN của bt là \(\frac{7}{2}\)