问题
填空题
对任意实数x,都有(x-1)4=a0+a1(x-3)+a(x-3)2+a3(x-3)3+a4(x-3)4,则
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答案
∵(x-1)4=[2+(x-3)]4=a0+a1(x-3)+a(x-3)2+a3(x-3)3+a4(x-3)4,
∴a1=
•23=32,a3=C 14
•2=8,∴C 34
=a1+a3 a3
=5,32+8 8
故答案为:8.
对任意实数x,都有(x-1)4=a0+a1(x-3)+a(x-3)2+a3(x-3)3+a4(x-3)4,则
|
∵(x-1)4=[2+(x-3)]4=a0+a1(x-3)+a(x-3)2+a3(x-3)3+a4(x-3)4,
∴a1=
•23=32,a3=C 14
•2=8,∴C 34
=a1+a3 a3
=5,32+8 8
故答案为:8.