初三数学题有点难

来源：百度知道 编辑：UC知道 时间：2024/05/12 18:48:46
X/(Y-Z)+Y/(Z-X)+Z/(X-Y)=0
求证
X/(Y-Z)^2+Y/(Z-X)^2+Z/(X-Y)^2=0
通过上面求证下面^2是……的2次方
X/(Y-Z)^2+Y/(Z-X)^2+Z/(X-Y)^2=0

X/(Y-Z)=-Y/(Z-X)-Z/(X-Y)
所以X/(Y-Z)^2
=-Y/(Z-X)(Y-Z)-Z/(X-Y)(Y-Z)
=[-Y(X-Y)-Z(Z-X)]/(X-Y)(Y-Z)(Z-X)
=(Y+Z-X)/(X-Y)(Z-X)
同理
Y/(Z-X)^2=-Z/(X-Y)(Z-X)-X/(Y-Z)(Z-X)
Z/(X-Y)^2=-X/(Y-Z)(X-Y)-Y/(Z-X)(X-Y)

所以
X/(Y-Z)^2+Y/(Z-X)^2+Z/(X-Y)^2
=(Y+Z-X)/(X-Y)(Z-X)-Z/(X-Y)(Z-X)-X/(Y-Z)(Z-X)-X/(Y-Z)(X-Y)-Y/(Z-X)(X-Y)
=-X/(X-Y)(Z-X)-X/(Y-Z)(Z-X)-X/(Y-Z)(X-Y)
=-X/(Z-X)[1/(X-Y)+1/(Y-Z)]-X/(Y-Z)(X-Y)
=X/(Y-Z)(X-Y)-X/(Y-Z)(X-Y)
=0

我不会

X、Y、Z的取值范围？