已知实数x,y满足x*2+xy+y*2=3,x+2y的最大值?

题目

已知实数x,y满足x*2+xy+y*2=3,x+2y的最大值?

答案

x^2+xy+y^2=3
设t=x+2y
x=t-2y
(t-2y)^2+(t-2Y)y+y^2=3
t^2-4yt+4y^2+ty-2y^2+y^2=3
3y^2-(4t-t)y+t^2-3=0
3y^2-(3t)y+t^2-3=0
deta>=0
9t^2-12(t^2-3)>=0
-3t^2+36>=0
t^2