- 二项式若（X^2+1）(X
- 若（X^2+1）(X-2)^9=a0+a1(x-1)+a2(x-1)^2+……+an(x-1)^n,则(a1+3a3+……+11a11)^2-(2a2+4a4+……+10a10)^2=?
题目很难写出来，希望大家帮帮忙啊！谢谢了
- f(x)=(x^2+1)(x-2)^9对x求导，就是
f'(x)=a1+2a2(x-1)+3a3(x-1)^2+...+nan(x-1)^(n-1)
=2x(x-2)^9+9(x^2+1)(x-2)^8
可知，f'(2)=0。
(a1+3a3+……+11a11)^2-(2a2+4a4+……+10a10)^2
=[(a1+3a3+……+11a11)+(2a2+4a4+……+10a10)]*[(a1+3a3+……+11a11)-(2a2+4a4+……+10a10)]
=f'(2)*f'(0)=0.