A rational number x equals its own reciprocal, and x is also a rational number (x = 1/x). How many such rational numbers exist, and what are they?

Question

Accepted Answer

Two: 1 and -1. x = 1/x gives x^2 = 1, so x = 1 or x = -1. Both are rational, so there are exactly two such numbers.

A rational number $x$ equals its own reciprocal, and $x$ is also a rational number $(x = \frac{1}{x})$ .
How many such rational numbers exist, and what are they?