x>0,y>0,2/(x+1)/y=1,若x+2y>m的平方+2m恒成立,则实数M的取值范围

2=xy+y,2/y-1=x
x+2y>m^2+2m
2/y+2y>(m+1)^2
2+2y^2>(m+1)^2y
2y^2-y(m+1)^2+2>0
y^2-[(m+1)^2/2]y+1>0
[y-(m+1)^2/4]^2+1-(m+1)^4/16>0
2^4=16>(m+1)^4
m+1<-2和m+1>2
m<-3和m>1即为满足x+2y>m^2+2m恒成立的实数m的取值范围