一道有争议的题目,已知a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)=(a+c)/b+(a+b)/c+(b+c)/a=(-b)/b+(-c)/c+(-a)/a=-1-1-1=-3.∵a+b+c=0∴a+b=-c,a+c=-b,b+c
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![一道有争议的题目,已知a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)=(a+c)/b+(a+b)/c+(b+c)/a=(-b)/b+(-c)/c+(-a)/a=-1-1-1=-3.∵a+b+c=0∴a+b=-c,a+c=-b,b+c](/uploads/image/z/11721892-4-2.jpg?t=%E4%B8%80%E9%81%93%E6%9C%89%E4%BA%89%E8%AE%AE%E7%9A%84%E9%A2%98%E7%9B%AE%2C%E5%B7%B2%E7%9F%A5a%2Bb%2Bc%3D0%2C%E6%B1%82a%281%2Fb%2B1%2Fc%29%2Bb%281%2Fc%2B1%2Fa%29%2Bc%281%2Fa%2B1%2Fb%29%E7%9A%84%E5%80%BCa%281%2Fb%2B1%2Fc%29%2Bb%281%2Fa%2B1%2Fc%29%2Bc%281%2Fa%2B1%2Fb%29%3D%28a%2Fb%2Bc%2Fb%29%2B%28a%2Fc%2Bb%2Fc%29%2B%28b%2Fa%2Bc%2Fa%29%3D%28a%2Bc%29%2Fb%2B%28a%2Bb%29%2Fc%2B%28b%2Bc%29%2Fa%3D%28-b%29%2Fb%2B%28-c%29%2Fc%2B%28-a%29%2Fa%3D-1-1-1%3D-3.%E2%88%B5a%EF%BC%8Bb%EF%BC%8Bc%EF%BC%9D0%E2%88%B4a%EF%BC%8Bb%EF%BC%9D%EF%BC%8Dc%2Ca%EF%BC%8Bc%EF%BC%9D%EF%BC%8Db%2Cb%EF%BC%8Bc)
一道有争议的题目,已知a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)=(a+c)/b+(a+b)/c+(b+c)/a=(-b)/b+(-c)/c+(-a)/a=-1-1-1=-3.∵a+b+c=0∴a+b=-c,a+c=-b,b+c
一道有争议的题目,
已知a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值
a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)=(a+c)/b+(a+b)/c+(b+c)/a=(-b)/b+(-c)/c+(-a)/a=-1-1-1=-3.
∵a+b+c=0
∴a+b=-c,a+c=-b,b+c=-a
∴原式=-a²/bc-b²/ac-c²/ab+3
=-(a³+b³+c³-3abc)/abc
=-[(a+b)³+c³-3a²b-3ab²-3abc]/abc
=-[(a+b+c)(a²+b²+2ab-ac-bc+c²-3ab(a+b+c)]/abc
=-(a+b+c)(a²+b²+2ab-ac-bc+c²-3ab)/abc
=0.
一道有争议的题目,已知a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)=(a+c)/b+(a+b)/c+(b+c)/a=(-b)/b+(-c)/c+(-a)/a=-1-1-1=-3.∵a+b+c=0∴a+b=-c,a+c=-b,b+c
第一步最后面的 +3 是哪里来的?所以答案 0 是错的:
原式=-a²/bc-b²/ac-c²/ab+3 ?
应该是:
原式 =-a²/bc-b²/ac-c²/ab +3 -3
=-(a³+b³+c³-3abc)/abc -3
=-[(a+b)³+c³-3a²b-3ab²-3abc]/abc -3
=-[(a+b+c)(a²+b²+2ab-ac-bc+c²-3ab(a+b+c)]/abc -3
=-(a+b+c)(a²+b²+2ab-ac-bc+c²-3ab)/abc -3
= -3