Question

因式分解竞赛题!急设有理数a,b,c 都不为零,且a+b+c=01 1 1则 _____________________

Answer 1

a+b+c=0

a+b=-c

(a+b)^2=c^2

a^2+b^2-c^2=-2ab

同理

c^2+a^2-b^2=-2ac

b＾2+c^2-a^2=-2bc

原式＝-1/2[1/(ab)+1/(bc)+1/(ac)]

=-1/2(a+b+c)/(abc)

=0