a+b+c=0 a^3+b^3+c^3=0 证明：对任意正奇数n,有a^n+b^n+c^n=0
问题描述：
a+b+c=0 a^3+b^3+c^3=0 证明：对任意正奇数n,有a^n+b^n+c^n=0
答
c=-a-bc^3=-a^3-3a^2b-3ab^2-b^3所以a^3+b^3-a^3-3a^2b-3ab^2-b^3=03ab(a+b)=0a=0或b=0或a+b=0若a=0,则c=-bn是奇数,(-b)^n=-b^n,a^n+b^n+c^n=0+b^n-b^n=0同理b=0也一样若a+b=0,则c=0,b=-a,a^n+b^n+c^n=a^n-a^n+0=0综...