Question

已知a,b,c为非零实数,且满足a2+b2+c2=1,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3求a+b+

求a+b+c的值

Answer 1

展开~~得（a+c)/b+(a+b)/c+(b+c)/a=-3
得（a+b+c)/b-1+(a+b+c)/c-1+(a+b+c)/a-1=-3
得（a+b+c)(1/b+1/a+1/c)=0
所以a+b+c=0