f(x)=ax²+bx+cf(x+1)+f(x-1)=a(x+1)²+b(x+1)+c+a(x-1)²+b(x-1)+c=2ax²+2bx+2a+2c=2x^2+4x所以2a=2,2b=4,2a+2c=0a=1,b=2,c=-1所以f(x)=x²+2x-1