设f(x)=ax^2+bx+c,则f(x+1)+f(x-1)=a[(x+1)^2+(x-1)^2]+b(x+1+x-1)+2c=2ax^2+2bx+2a+2c=2x^2-4x,比较系数得a=1,b=-2,2a+2c=0,c=-1,∴f(x)=x^2-2x-1.
