已知非零a+b+c=0,实数abc满足a+b+c不等于零,a^2+b^2+c^=1,a(1/b+1/c)已知非零实数abc满足a+b+c不等于零,a^2+b^2+c^=1,a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=-3,求a+b+c的值
问题描述:
已知非零a+b+c=0,实数abc满足a+b+c不等于零,a^2+b^2+c^=1,a(1/b+1/c)
已知非零实数abc满足a+b+c不等于零,a^2+b^2+c^=1,a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=-3,求a+b+c的值
答
999
答
(a+b+c)^2=a^2+b^2+c^+2ab+2ac+2bc =1+2ab+2ac+2bcab+ac+bc=[(a+b+c)^2-1]/2设a+b+c=kab+ac+bc=(k^2-1)/2a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)=-3a(1/b+1/c)+1+b(1/a+1/c)+1+c(1/a+1/b)+1=0(ab+ac+...