已知abc不等于0,且满足a+b+c=0 求a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)的值
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![已知abc不等于0,且满足a+b+c=0 求a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)的值](/uploads/image/z/438267-3-7.jpg?t=%E5%B7%B2%E7%9F%A5abc%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3a%2Bb%2Bc%3D0+%E6%B1%82a%28b%2F1%2Bc%2F1%29%2Bc%28a%2F1%2Bb%2F1%29%2Bb%28a%2F1%2Bc%2F1%29%E7%9A%84%E5%80%BC)
已知abc不等于0,且满足a+b+c=0 求a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)的值
已知abc不等于0,且满足a+b+c=0 求a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)的值
已知abc不等于0,且满足a+b+c=0 求a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)的值
a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)
=a(a/1+b/1+c/1)+c(c/1+a/1+b/1)+b(b/1+a/1+c/1)-a*a/1-b*b/1-c*c/1
=(a+b+c)(a/1+b/1+c/1))-a*a/1-b*b/1-c*c/1 因为a+b+c=0
=-a*a/1-b*b/1-c*c/1
=-3
a(1/b+1/c)+c(1/a+1/b)+b(1/a+1/c)
=(a+b)/c+(a+c)/b+(b+c)/a
=-c/c-b/b-a/a
=-1-1-1
=-3
b/1不是等于b吗,直接写b不就得了?还是你写错了?
a(b/1+c/1)+c(a/1+b/1)+b(a/1+c/1)
=a(a/1+b/1+c/1)+c(c/1+a/1+b/1)+b(b/1+a/1+c/1)-a*a/1-b*b/1-c*c/1
=(a+b+c)(a/1+b/1+c/1))-a*a/1-b*b/1-c*c/1 因为a+b+c=0
=-a*a/1-b*b/1-c*c/1
=-3