已知非零实数a,b,c满足a^+b^+c^=1,且a(1/b+1/c）+b(1/c+1/a)+c(1/a+1/b）=-3,求a+b+c的值?

题目

已知非零实数a,b,c满足a^+b^+c^=1,且a(1/b+1/c）+b(1/c+1/a)+c(1/a+1/b）=-3,求a+b+c的值?

答案

a(1/b+1/c）+b(1/c+1/a)+c(1/a+1/b）=-3=>a(1/b+1/c）+b(1/c+1/a)+c(1/a+1/b）+3=0=>a/b+a/c+b/b+b/a+c/a+c/b+3=0=>(a+b+c)/b+(a+b+c)/a+(a+b+c)/c=0=>(a+b+c)(ab+bc+ca)/abc=0则因a,b,c为非0实数,a+b+c=0,or,ab+bc+...