x，y，z为正实数，且满足xyz=1，x+1y=5，y+1z=29，则z+1x的值为1414．

Question

x，y，z为正实数，且满足xyz=1，x+(1)/(y)=5，y+(1)/(z)=29，则z+(1)/(x)的值为

(1)/(4)

(1)/(4)

．

Answer 1

（x+(1)/(y)）（y+(1)/(z)）（z+(1)/(x)）
=（x+y+z）+xyz+(1)/(xyz)+（(1)/(x)+(1)/(y)+(1)/(z)）
=2+（x+(1)/(y)）+（y+(1)/(z)）+（z+(1)/(x)），
∴5×29×（z+(1)/(x)）=36+（z+(1)/(x)），
  即 z+(1)/(x)=(1)/(4)．
故答案为：(1)/(4)．