已知2a/(3b+3c)=2b/(3c+3a)=2c/(3a+3b)=k求k的值

问题描述:

已知2a/(3b+3c)=2b/(3c+3a)=2c/(3a+3b)=k求k的值

2a/(3b+3c)=2b/(3c+3a)=2c/(3a+3b)=k
(2/3)×a/(b+c)=k
a²+ac=b²+bc ①
a²+ab=c²+bc ②
b²+ab=c²+ac ③
①-②,得出:a(c-b)=b²-c²=(b+c)(b-c)
∴b+c=-a即a/(b+c)=-1
k=-2/3