x+1/y=1,y+1/z=1,求xyz,为什么xyz会等于-1呢?难道x,y,z不应该都大于零么

题目

x+1/y=1,y+1/z=1,求xyz,为什么xyz会等于-1呢?难道x,y,z不应该都大于零么

答案

x+1/y=1
x=1-1/y
y+1/z=1
z=1/(1-y)
xyz=(1-1/y)*y*[1/(1-y)]
=[(y-1)/y]*y*[1/(1-y)]
=[-(1-y)/y]*y*[1/(1-y)]
=[-(1-y)*[1/(1-y)]
=-1