设实数X,Y,Z,满足X+1/y=1,y+1/z=1,则xyz的值为?

问题描述:

设实数X,Y,Z,满足X+1/y=1,y+1/z=1,则xyz的值为?

由x+1/y=1可求y=1/(1-x),由y+1/z=1和y=1/(1-x)可求z=(x-1)/x,则xyz=-1.

1/y=1-x
y=1/﹙1-x﹚
1/﹙1-x﹚+1/z=1
1/z=1-1/﹙1-x﹚=﹣x/﹙1-x﹚
z=﹙1-x﹚/﹙﹣x﹚
∴xyz=x·1/﹙1-x﹚·﹙1-x﹚/﹙﹣x﹚=﹣1