〖求£证〗

若a+b+c=0,求证:1/(b^2+c^2-a^2)+1/(c^2+a^2-b^2)+1/(a^2+b^2-c^2)=0
2025-03-24 11:28:54
推荐回答(1个)
回答1:

a+b+c=0
a+b=-c
(a+b)^2=c^2
a^2+b^2-c^2=-2ab
同理:b^2+c^2-a^2=-2bc,c^2+a^2-b^2=-2ac

1/(b^2+c^2-a^2)+1/(c^2+a^2-b^2)+1/(a^2+b^2-c^2)
=-1/(2bc)-1/(2ac)-1/(2ab)
=-(a+b+c)/(2abc)
=0