Question

If xyz=1 ,x+1/z=5 ,y+1/x=29 ,then find z+1/y=

Answer 1

we can write x+(1/z) as (1/yz) + (1/z) solving this we get(1+y)/yz = 5 ................(1)

now from the second equation we get y + yz = 29

or, yz = 29-y putting it in (1) we get (1+y) = 5(29-y)

or, 1+y = 145 - 5y6y = 144or, y = 24now again putting it in (1) we get 25 = 120z

or, z = 5/24so x = 1/yz or, x = 1/5 notice that this fulfills the requirement xyz = 1so now z + 1/x = z + zy = 5/24 + (5/24)(1/5) = 5/24 + 1/24 = 1/4