对任意实数x,有x3=a0+a1(x−2)+a2(x−2)2+a3(x−2)3,则a2=(  ) A.3 B.6 C.9 D.21

问题描述:

对任意实数x,有x3a0+a1(x−2)+a2(x−2)2+a3(x−2)3,则a2=(  )
A. 3
B. 6
C. 9
D. 21

根据题意,x3a0+a1(x−2)+a2(x−2)2+a3(x−2)3
而x3=[(x-2)+2]3=C30(x-2)023+C3122(x-2)+C3221(x-2)2+C3320(x-2)3
则a2=C3221=6;
故选B.