Question

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

Answer 1

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