已知a,b,c均为非零的实数,且满足a+b-c/c=a-b+c/b=-a+b+c/a,求(a+b)(b+c)(c+a)/abc的值

由比例关系,(a＋b－c)/c＝(a－b＋c)/b＝(－a＋b＋c)/a＝((a＋b－c)＋(a－b＋c)＋(－a＋b＋c))/(a＋b＋c)＝(a+b+c)/(a+b+c)＝1所以,a＋b－c＝c,a－b＋c＝b,－a＋b＋c＝a,即a＋b＝2c,a＋c＝2b,b＋c＝2a所以,(a+b)(b+c)...