已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k的值

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已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k的值已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k的值已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k

已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k的值
已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k的值

已知x.y.z.满足y+z/x=z+x/y=x+y/z=k,求k的值
已知x,y,z满足y+z/x=z+x/y=x+y/z=k,求k的值
解:∵ y+z/x=z+x/y=x+y/z=k
∴ y+z/x=k z+x/y=k x+y/z=k
∴ kx=y+z
ky=x+z
kz=x+y
∴kx+kz+ky=2(x+y+z)
k(x+y+z)=2(x+y+z)
k=2

-1

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