x、y∈R,u=x^2+xy+y^2-x-2y+3 =x^2+(y-1)x+y^2-2y+3 =[x+(y-1)/2]^2+y^2-2y+3-(y-1)^2/4 =[x+(y-1)/2]^2+(1/4)(3y^2-6y+11) =[x+(y-1)/2]^2+(3/4)(y-1)^2+2,当x=0,y=1时u取最小值2.