已知y+1⼀z=1,z+1⼀x=1,试证明x+1⼀y=1

2025-03-26 06:28:22
推荐回答(1个)
回答1:

由y+1/z=1,得
1/z= 1-y
z=1/(1-y)= (1-y+y)/(1-y)= 1+ y/(1-y)

将其代入z+1/x=1,得
1+y/(1-y)+1/x = 1
则: y/(y-1)=1/x
则: x= (y-1)/y= 1- 1/y,

即: x + 1/y = 1