分类：教育/科学-理工学科-数学
问题：x、y∈R,求u=x^2+xy+y^2
回答：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.