2a²＋bc=2a²－c(a＋c)=2a²－ac－c²=(a－c)(2a＋c)=(a－c)(a－b),
同理有：2b²＋ca=(b－c)(b－a),2c²＋ab=(c－a)(c－b).
∴a^2/(2a^2+bc)+b^2/(2b^2+ac)+c^2/(2c^2+ab)
＝a^2/(a-b)(a-c)+b^2/(b-a)(b-c)+c^2/(c-a)(c-b)
=[a^2(b-c)-b^2(a-c)+c^2(a-b)]/(a-b)(a-c)(b-c)
分子分母都展开
=[ a^2b- a^2 c-b^2a+ b^2c+c^2a- c^2b]/ [ a^2b-abc-b^2a + b^2c - a^2 c+c^2a+abc- c^2b]
=[ a^2b- a^2 c-b^2a+ b^2c+c^2a- c^2b]/ [ a^2b- a^2 c-b^2a+ b^2c+c^2a- c^2b]
=1