c/(a+b)=b/(a+c)=a/(b+c)=A,求A的值.答案是1/2和—1,怎么算出-1呢?

c/(a+b)=b/(a+c)=a/(b+c)=A,求A的值.答案是1/2和—1,怎么算出-1呢?
c/(a+b)=b/(a+c)=a/(b+c)=A,求A的值.答案是1/2和—1,怎么算出-1呢?

c/(a+b)=b/(a+c)=a/(b+c)=A,求A的值.答案是1/2和—1,怎么算出-1呢?
c/(a+b)=b/(a+c)=a/(b+c)=A
c=Aa+Ab
b=Aa+Ac
a=Ab+Ac
相加
a+b+c=2A(a+b+c)
(a+b+c)(2A-1)=0
若a+b+c=0
则a+b=-c
A=c/(-c)=-1
若2A-1=0
则A=1/2
所以A=-1或1/2