G=x2−2xy+2y2+2x−10y+17=x2−2xy+y2+y2+2x−2y−8y+1+16=(x2+y2+1−2xy+2x−2y)+(y2−8y+16)=(x−y+1)2+(y−4)2
Do (x−y+1)2≥0∀x;y
(y−4)2≥0∀y
⇒G=(x−y+1)2+(y−4)2≥0∀x;y
Dấu "=" xảy ra khi: {(x−y+1)2=0(y−4)2=0⇔{x−y+1=0y−4=0
⇔{x=y−1y=4⇔{x=3y=4
Vậy G(Min)=0 khi {x=3y=4
