已知a,b,c都是有理数,满足:a(1/b + 1/c)+ b(1/a + 1/c)+ c(1/a + 1/b)=-3且a+b+c不为0求:1/a + 1/b + 1/c的值
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![已知a,b,c都是有理数,满足:a(1/b + 1/c)+ b(1/a + 1/c)+ c(1/a + 1/b)=-3且a+b+c不为0求:1/a + 1/b + 1/c的值](/uploads/image/z/14386721-41-1.jpg?t=%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%E9%83%BD%E6%98%AF%E6%9C%89%E7%90%86%E6%95%B0%2C%E6%BB%A1%E8%B6%B3%EF%BC%9Aa%281%2Fb+%2B+1%2Fc%29%2B+b%281%2Fa+%2B+1%2Fc%29%2B+c%281%2Fa+%2B+1%2Fb%29%3D-3%E4%B8%94a%2Bb%2Bc%E4%B8%8D%E4%B8%BA0%E6%B1%82%EF%BC%9A1%2Fa+%2B+1%2Fb+%2B+1%2Fc%E7%9A%84%E5%80%BC)
已知a,b,c都是有理数,满足:a(1/b + 1/c)+ b(1/a + 1/c)+ c(1/a + 1/b)=-3且a+b+c不为0求:1/a + 1/b + 1/c的值
已知a,b,c都是有理数,满足:
a(1/b + 1/c)+ b(1/a + 1/c)+ c(1/a + 1/b)=-3
且a+b+c不为0
求:1/a + 1/b + 1/c的值
已知a,b,c都是有理数,满足:a(1/b + 1/c)+ b(1/a + 1/c)+ c(1/a + 1/b)=-3且a+b+c不为0求:1/a + 1/b + 1/c的值
a(1/b + 1/c)+ b(1/a + 1/c)+ c(1/a + 1/b)=-3
由乘法分配律
a/b+a/c+b/a+b/c+c/a+c/b+3=0
a/b+a/c+b/a+b/c+c/a+c/b+1+1+1=0
(a/b+c/b+1)+(b/a+c/a+1)+(a/c+b/c+1)=0
(a+b+c)/b+(a+b+c)/a+(a+b+c)/c=0
(a+b+c)(1/a+1/b+1/c)=0
a+b+c≠0
所以1/a+1/b+1/c=0