已知a,b,c为有理数,满足ab+ac+bc不等于0,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3,求a+b+c的值
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![已知a,b,c为有理数,满足ab+ac+bc不等于0,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3,求a+b+c的值](/uploads/image/z/1683622-46-2.jpg?t=%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%E4%B8%BA%E6%9C%89%E7%90%86%E6%95%B0%2C%E6%BB%A1%E8%B6%B3ab%2Bac%2Bbc%E4%B8%8D%E7%AD%89%E4%BA%8E0%2Ca%281%2Fb%2B1%2Fc%29%2Bb%281%2Fc%2B1%2Fa%29%2Bc%281%2Fa%2B1%2Fb%29%3D-3%2C%E6%B1%82a%2Bb%2Bc%E7%9A%84%E5%80%BC)
已知a,b,c为有理数,满足ab+ac+bc不等于0,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3,求a+b+c的值
已知a,b,c为有理数,满足ab+ac+bc不等于0,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3,求a+b+c的值
已知a,b,c为有理数,满足ab+ac+bc不等于0,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3,求a+b+c的值
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)+3=0
a(1/a+1/b+1/c)+b(1/b+1/c+1/a)+c(1/c+1/a+1/b)=0
(a+b+c)(1/a+1/b+1/c)=0
(a+b+c)(ab+bc+ca)/abc=0
ab+ac+bc不等于0
所以,a+b+c=0