Q13/078) Let x,y, and z be distinct non-zero real numbers such that x+1/y=y+1/z=z+1/x. What is the value of |xyz|?

x+1/y=y+1/z=z+1/x. ...(1)

now putting 1/a for z , 1/b for x and 1/c for y we get

1/b + c = 1/c + a = 1/a + b

the above equation is same as (1) with c for x b for y and a for z and hence

|xyz| = |abc| as the value is unique

= | 1/z 1/x 1/y| = | 1/xyz|

so |xyz| = 1