x,y∈R+,且x+2y=1,求xy
问题描述：
x,y∈R+,且x+2y=1,求xy
答
x=1-2y
xy
=(1-2y)y
=2y(1-2y)/2
≤[(2y+1-2y)/2]^2/2
=1/8
当且仅当2y=1-2y,也就是y=1/4时取等号
此时x=1/2