设二次函数f(x)满足f(x+1)+f(x-1)=2x^2-4x,
问题描述:
设二次函数f(x)满足f(x+1)+f(x-1)=2x^2-4x,
答
令f(x)=ax^2+bx+c
则f(x+1)+f(x-1)=2a(x^2+1)+2bx+2c=2x^2-4x
对比系数得:2a=2,2b=-4,2a+2c=0
解得:a=1,b=-2,c=-1
故f(x)=x^2-2x-1