令2009-a=x-1,则2011-a=x+1 (x-1)(x+1)=1000 x^2-1=1000 x^2=1001 (2011-a)^2+(2009-a)^2 =(x+1)^2+(x-1)^2 =x^2+2x+1+x^2-2x+1 =2x^2+2 =2002+2 =2004