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x/(y+z+u)=y/(z+u+x)=z/(u+y+x)=u(x+y+z)求(x+y)/(z+u)+(y+z)/(y+x)+(z+y)/(x+y)+(u+x)/(z+y)
题目详情
x/(y+z+u)=y/(z+u+x)=z/(u+y+x)=u(x+y+z)求(x+y)/(z+u)+(y+z)/(y+x)+(z+y)/(x+y)+(u+x)/(z+y)
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答案和解析
题目是否几处有错?
x/(y+z+u)=y/(z+u+x)=z/(u+y+x)=u / (x+y+z)
求(x+y)/(z+u)+(y+z)/( u +x)+(z+ u )/(x+y)+(u+x)/(z+y)
x/(y+z+u)=y/(z+u+x)
x(z+u+x)=y(y+z+u)
(x-y)(z+u)=y^2-x^2=(y-x)(y+x)
(x+y)/(z+u)=-1
同理可得(y+z)/( u +x)=(z+ u )/(x+y)=(u+x)/(z+y)=-1
(x+y)/(z+u)+(y+z)/( u +x)+(z+ u )/(x+y)+(u+x)/(z+y)=-4
x/(y+z+u)=y/(z+u+x)=z/(u+y+x)=u / (x+y+z)
求(x+y)/(z+u)+(y+z)/( u +x)+(z+ u )/(x+y)+(u+x)/(z+y)
x/(y+z+u)=y/(z+u+x)
x(z+u+x)=y(y+z+u)
(x-y)(z+u)=y^2-x^2=(y-x)(y+x)
(x+y)/(z+u)=-1
同理可得(y+z)/( u +x)=(z+ u )/(x+y)=(u+x)/(z+y)=-1
(x+y)/(z+u)+(y+z)/( u +x)+(z+ u )/(x+y)+(u+x)/(z+y)=-4
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