已知a,b,c为有理数,且满足a^2+b^2+c^2=1,a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3,求a+b+c的值

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+