X=\Y=\Z,x+1/y=y+1/z=z+1/x,求XYZ的平方如题X=\Y=\Z(=\是不等于)
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X=\Y=\Z,x+1/y=y+1/z=z+1/x,求XYZ的平方如题X=\Y=\Z(=\是不等于)
X=\Y=\Z,x+1/y=y+1/z=z+1/x,求XYZ的平方
如题
X=\Y=\Z(=\是不等于)
X=\Y=\Z,x+1/y=y+1/z=z+1/x,求XYZ的平方如题X=\Y=\Z(=\是不等于)
∵x、y、z不等,∴x-y、y-z、x-z都不为0.
∵x+1/y=y+1/z=z+1/x.
∴由x+1/y=y+1/z,得:x-y=1/z-1/y=(y-z)/(yz),∴yz=(y-z)/(x-y).···①
由x+1/y=z+1/x,得:x-z=1/x-1/y=(y-x)/(xy),∴xy=(y-x)/(x-z).···②
由y+1/z=z+1/x,得:y-z=1/x-1/z=(z-x)/(xz),∴xz=(z-x)/(y-z).···③
①、②、③三式相乘,得:(xyz)^2=1.
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