Question

若a+b+c=0,求(bc分之a^2)+（ac分之b^2)+（ab分之c^2)的值

Answer 1

a^2/(bc)＝(b＋c)^2/(bc)＝b/c＋c/b＋2

b^2/(ac)＝(a＋c)^2/(ac)＝a/c＋c/a＋2

c^2/(ab)＝(b＋a)^2/(ab)＝b/a＋a/b＋2

三式相加得：

原式＝(b/c＋a/c)＋(c/b＋a/b)＋(c/a＋b/a)＋6

＝(b＋a)/c＋(c＋a)/b＋(c＋b)/a＋6

＝(－c)/c＋(－b)/b＋(－a)/a＋6

＝3