已知2a/(3b+3c)=2b/(3c+3a)=2c/(3a+3b)=k求k的值
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已知2a/(3b+3c)=2b/(3c+3a)=2c/(3a+3b)=k求k的值
![已知2a/(3b+3c)=2b/(3c+3a)=2c/(3a+3b)=k求k的值](/uploads/image/z/2926182-30-2.jpg?t=%E5%B7%B2%E7%9F%A52a%2F%283b%2B3c%29%3D2b%2F%283c%2B3a%29%3D2c%2F%283a%2B3b%29%3Dk%E6%B1%82k%E7%9A%84%E5%80%BC)
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
(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
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