2n²+m²+4n-4m+6=0
(2n²+4n+2)+(m²-4m+4)=0
2(n+1)²+(m-2)²=0
两项均为非负值,和为0,则它们均为0
∴n+1=0且m-2=0
∴n=-1,m=2
∴m+n=1
∴(n+m)^2008=1