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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
题目详情
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
▼优质解答
答案和解析
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
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
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