若x、y、z满足 y+z/x=z+x/y=x+y/z=k 求k的值
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![若x、y、z满足 y+z/x=z+x/y=x+y/z=k 求k的值](/uploads/image/z/13336619-59-9.jpg?t=%E8%8B%A5x%E3%80%81y%E3%80%81z%E6%BB%A1%E8%B6%B3+y%2Bz%2Fx%3Dz%2Bx%2Fy%3Dx%2By%2Fz%3Dk+%E6%B1%82k%E7%9A%84%E5%80%BC)
若x、y、z满足 y+z/x=z+x/y=x+y/z=k 求k的值
若x、y、z满足 y+z/x=z+x/y=x+y/z=k 求k的值
若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
不对吧。
设x=y=z=1==>k=2
设x=y=z=2==>k=3
......
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