若实数x，y，z，满足：x+1y=1，y+1z=1，则xyz的值为（）A.1B.2C.-1D.-2

Question

若实数x，y，z，满足：x+(1)/(y)=1，y+(1)/(z)=1，则xyz的值为（　　）
A. 1
B. 2
C. -1
D. -2

Answer 1

∵x+(1)/(y)=1，y+(1)/(z)=1，
∴x=1-(1)/(y)=(y−1)/(y)，(1)/(z)=1-y，
∴z=(1)/(1−y)，
∴xyz
=(y−1)/(y)×y×(1)/(1−y)
=-1，
故选C．