设f(x)=ax的平方+bx+c(a,b,c均为常数).计算f(x+3)-3f(x+2)+3f(x+1)-f(x)的值.

问题描述:

设f(x)=ax的平方+bx+c(a,b,c均为常数).计算f(x+3)-3f(x+2)+3f(x+1)-f(x)的值.

f(x+3)-f(x)=a(x+3)²+b(x+3)+c-ax²-bx-c=a(x+3)²-ax²+3b=3a(2x+3)+3bf(x+2)-f(x+1)=a(x+2)²+b(x+2)+c-a(x+1)²-b(x+1)-c=a(2x+3)+b原式=[f(x+3)-f(x)]-3[f(x+2)-f(x+1)]=3a(2x+3)+3b-...