Question

若（2x-1）的五次方=a5x的五次方+a4x的四次方+a3x的三次方+a2x的二次方+a1x+a0,若x=0时,有何结

Answer 1

a0、a1、a2……都是系数吧?

(2x-1)^5=(a5)x^5+(a4)x^4+(a3)x^3+(a2)x^2+(a1)x+a0

1、当x=0时,有：

(2×0-1)^5=(a5)×0^5+(a4)×0^4+(a3)×0^3+(a2)×0^2+(a1)×0+a0

a0=-1

2、当x=1时,有：

(2×1-1)^5=(a5)×1^5+(a4)×1^4+(a3)×1^3+(a2)×1^2+(a1)×1+a0

(a5)+(a4)+(a3)+(a2)+(a1)+a0=1

2、当x=-1时,有：

[2×(-1)-1]^5=(a5)×(-1)^5+(a4)×(-1)^4+(a3)×(-1)^3+(a2)×(-1)^2+(a1)×(-1)+a0

(-3)^5=-(a5)+(a4)-(a3)+(a2)-(a1)+a0

-(a5)+(a4)-(a3)+(a2)-(a1)+a0=-243