查人人中国名人网学生会部门介绍ppt模板:初一数学
来源：百度文库 编辑：查人人中国名人网 时间：2024/05/03 09:59:53
a+b=0,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=______
错了吧？应该是a+b+c=0
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a/b+a/c+b/c+b/a+c/a+c/b
=(a+c)/b+(a+b)/c+(b+c)/a
=-b/b-c/c-a/a
=-1-1-1
=-3
=0
-2
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a/b+a/c+b/c+b/a+c/a+c/b
=(a+c)/b+(a+b)/c+(b+c)/a
=(a+c)/b+(b+c)/a
因为a+b=0,所以a=-b.
(a+c)/b+(b+c)/a
=(a+c)/b-(b+c)/b
=(a-b)/b
=-2b/b
=-2
对吧
等于正负3吧？？
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a/b+a/c+b/c+b/a+c/a+c/b
=(a/b+b/a)+(a/c+c/a)+(b/c+c/b)
=(a2+b2)/ab+(a2+c2)/ac+(b2+c2)/bc
(a2是a的平方的意思）
因为，a+b=0-----a2+b2+a+2ab=0
原式=-2+(a2+c2)/ac+(b2+c2)/bc
=-2+(a2+c2)/ac+(a2+c2)/(-a)c
=-2+0=0.
也对吧