f(x)=ax^2+bx+c
f(x+1)+f(x-1)=a(x+1)^2+b(x+1)+c+a(x-1)^2+b(x-1)+c
=2ax^2+2bx+2a+2b+2c
=2x^2-4x
所以a=1,b=-2,c=1
f(x)=x^2-2x+1=(x-1)^2
f(1+√2)=(1+√2-1)^2=2