已知等式(x-3)*(x-3)*(x-3)*(x-3)*(x-3)*=ax*ax*ax*ax*ax*+bx*bx*bx*bx*+cx*cx*cx+dx*dx*+ex+f ,求a-b+c-d+e
问题描述:
已知等式(x-3)*(x-3)*(x-3)*(x-3)*(x-3)*=ax*ax*ax*ax*ax*+bx*bx*bx*bx*+cx*cx*cx+dx*dx*+ex+f ,求a-b+c-d+e
答
x为任意实数,当x=0时 (0-3)×(0-3)×(0-3)×(0-3)×(0-3)=ff=(-3)^5f=-243当x=-1时(-4)^5=-a+b-c+d-e+f-1024+243=-a+b-c+d-e+f-f-781=-a+b-c+d-e-(-781)=a-b+c-d+e所以a-b+c-d+e=781...