已知：[a/(bc-a2)]+[b/(ac-b2)]+[(c/ab-c2)]=0求：[a/(bc-a2)2]+[b/(ac-b2)2]+[(c/ab-c2)2]的值.

Question

已知：[a/(bc-a2)]+[ b/(ac-b2)]+ [(c/ab-c2)]=0求：[a/(bc-a2)2]+[ b/(ac-b2) 2]+ [(c/ab-c2) 2] 的值.

Answer 1

先证明a+b+c=0
条件式中通分,分子=(a+b+c)(ab*bc+ab*ac+bc*ac-(ab)^2-(bc)^2-(ca)^2)=0
若a+b+c=0,得证.否则,(ab*bc+ab*ac+bc*ac-(ab)^2-(bc)^2-(ca)^2)=0可得ab=bc=ac,即a=b=c或a,b,c中有两个是0.若a=b=c则bc-a2=0,矛盾.
若a=b=0同理矛盾.所以a+b+c=0.
把a=-(b+c)代入欲求的式子即得答案为0.