财富给最快回答的朋友若(x-2)^2=a0+a1(x-1)+a2(x-1)^2+……a9(x-1)^9,求a8为多少.

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财富给最快回答的朋友若(x-2)^2=a0+a1(x-1)+a2(x-1)^2+……a9(x-1)^9,求a8为多少.

财富给最快回答的朋友若(x-2)^2=a0+a1(x-1)+a2(x-1)^2+……a9(x-1)^9,求a8为多少.
财富给最快回答的朋友
若(x-2)^2=a0+a1(x-1)+a2(x-1)^2+……a9(x-1)^9,求a8为多少.

财富给最快回答的朋友若(x-2)^2=a0+a1(x-1)+a2(x-1)^2+……a9(x-1)^9,求a8为多少.
(x-2)^9=(x-1-1)^9
=a0 + a1 (x-1) + a2 (x-1)^2 + ... + a9 (x-1)^9 ,
所以a8(x-1)^8=C(9,8)(x-1)^8*(-1)^1
=-C(9,1)(x-1)^8
=-9(x-1)^8
即a8=-9

0

x-2=x-1=2-ao9x(x-2=1) =a8=100

∵(x-2)²=(x-1-1)²
=(x-1)²-2(x-1)+1
当x=1时(1-2)²=a0=1
∴a1=-2,a2=1,a3=a4……=a8=a9=0

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