y=0时 f(x)=f(x)+2f²(0)
解得f(0)=0
x=0,y=1时
f(1)=f(0)+2f²(1)=2f²(1)
因f(1)不等于0
所以f(1)=1/2
y=1时 f(x+1)=f(x)+2*f²(1)=f(x)+2*(1/2)²
所以f(x+1)=f(x)+1/2
故f(2012)=f(2011+1)=f(2011)+1/2
=f(2010)+1/2+1/2=f(2010)+(1/2)*2
=.=f(1)+(1/2)*2011
=1/2+(1/2)*2011
=(1/2)*2012
=1006