a) $A=x^2-2x+10$
$=(x^2-2x+1)+9$
$=(x-1)^2+9\ge 9$
$B=x^2-3x+8$
$=x^2-2.\frac{3}{2}x+\frac{9}{4}+\frac{23}{4}$
$=(x-\frac{3}{2})^2+\frac{23}{4}\ge \frac{23}{4}$
$C=2x^2-5x+7$
$2C=4x^2-10x+14$
$=\left(4x^2-10x+\frac{25}{4}\right)+\frac{31}{4}$
$=(2x+\frac{5}{2})^2+\frac{31}{4}$
$⇒C=(2x+\frac{5}{2})^2:2+\frac{31}{4}:2\ge \frac{31}{8}$
$D=(x-1)^2+(x-3)^2+5\ge 5$
$E=(x^2-4x+1)^2-2(x^2-4x)+8$
$=(x^2-4x+1)^2-2(x^2-4+1)+1+9$
$=(x^2-4x)^2+9\ge 9$
$F=(x-2)^2+4|x-2|+5≥5$
$G=x^2-2xy+2y^2+10y+50$
$=(x^2-2xy+y^2)+(y^2+10y+25)+25$
$=(x-y)^2+(y+5)^2+25\ge 25$
$H=x^2-2xy+5y^2-4y+3$
$=(x^2-2xy+y^2)+(4y^2-4y+1)+2$
$=(x-y)^2+(2y-1)^2+2\ge 2$
