百度作业网X/(Y-Z)+Y/(Z-X)+Z/(X-Y)=0
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/06/23 14:38:56
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
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
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
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