x,y,z为正数,且满足xyz=1,x+1/z=5,y+1/x=29,求z+1/y的值

Question

x,y,z为正数,且满足xyz=1,x+1/z=5,y+1/x=29,求z+1/y的值

Answer 1

x = 1 / (yz)
代入另两式
y + yz = 29
1/(yz) + 1/z = 5
y = 24
z = 5/24
x = 1/5
z + 1/y = 6/24 = 1/4