分类：教育/科学-学习帮助
问题：初中2已知非零实数a.b.c.满足a*a+b*b+c*c=1,且 
已知非零实数a. b . c.满足a*a+b*b+c*c=1,且a(1/b+1c)+b(1/a+1/c)+c(1/a+1/b)=-3 ,求a+b+c的值
回答：解：根据题义有a(1/b+1c)+b(1/a+1/c)+c(1/a+1/b)=-3 
        即  a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)+3 =0
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)+3 
   =(b/a+c/a+1)+(a/b+c/b+1)+(a/c+b/c+1) 
   =(b/a+c/a+a/a)+(a/b+c/b+b/b)+(a/c+b/c+c/c) 
   =(a+b+c)/a+(a+b+c)/b+(a+b+c)/c
   =(a+b+c)(1/a+1/b+1/c)=0 

可得a+b+c=0,或1/a+1/b+1/c=0.
 
当1/a+1/b+1/c=0时.
1/a+1/b+1/c=(ab+bc+ac)/abc
a. b . c为非零实数，abc不等于0 则可推出ab+bc+ac=0 
(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac =1+0 =1
a+b+c=1或-1

所以a+b+c=1、-1或0.