a) $x^2-2x+5=(x-1)^2+4 ≥ 4$
Dấu "=" xảy ra $⇔x=1$
b) $x^2-x+1 = \bigg(x-\dfrac{1}{2}\bigg)^2+\dfrac{3}{4} ≥ \dfrac{3}{4}$
Dấu "=" xảy ra $⇔x=\dfrac{1}{2}$
c) $2x^2+6x-5$
$ = \dfrac{1}{2}.\bigg(4x^2+12x-10\bigg)$
$ = \dfrac{1}{2}.\bigg[(2x)^2+2.2x.3 + 9-19\bigg]$
$ = \dfrac{1}{2}.(2x+3)^2 - \dfrac{19}{2} ≥ \dfrac{19}{2}$
Dấu "=" xảy ra $⇔x=-\dfrac{3}{2}$
d) $4x^2-4x=(4x^2-4x+1)-1 = (2x-1)^2-1 ≥ -1$
Dấu "=" xảy ra $⇔x=\dfrac{1}{2}$