设(2x-1)5=ax5+bx4+cx3+dx2+ex+f,求b+d
问题描述:
设(2x-1)5=ax5+bx4+cx3+dx2+ex+f,求b+d
答
(2x-1)5=ax5+bx4+cx3+dx2+ex+f当x=1时,左边=(2*1-1)^5=1右边=a+b+c+d+e+f可得:1=a+b+c+d+e+f (1)当x=-1时,左边=(-2-1)^5=(-3)^5=-243右边=-a+b-c+d-e+f 可得:-243=-a+b-c+d-e+f (2)(1)+(2)可得:1-2...