英语 数学(分式) (11 11:26:51)
6个回答

a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3

a(1/b+1/c)+1+b(1/c+1/a)+1+c(1/a+1/b)+1=-3+3

a(1/a+1/b+1/c)+b(1/a+1/b+1/c)+c(1/a+1/b+1/c)=0

(a+b+c)*(1/a+1/b+1/c)=0

a+b+c=0

或1/a+1/b+1/c=0

(bc+ac+ab)/(abc)=0

ab+ac+bc=0

a^2+b^2+c^2=1

a^2+b^2+c^2+2ab+2ac+2bc=1+0

(a+b+c)^2=1

a+b+c=1或-1

综上所述a+b+c=0或1或-1