a,b,c为正整数,且(√3a+b)/(√3b+c)为有理数,求(a+b+c)/(a+b+c)的值.

问题描述:

a,b,c为正整数,且(√3a+b)/(√3b+c)为有理数,求(a+b+c)/(a+b+c)的值.

(√3a+b)(√3b-c)/(3b^2-c^2)=[3ab-bc+√3(-ac+b^2)]/(3b^2-c^2),(√3a+b)/(√3b+c)为有理数,ac=b^2,a,b,c成等比数列即可.(a+b+c)/(a+b+c)=a-b+c