Chapter 3 - Solving Inequalities - 3-1 Inequalities and Their Graphs - Practice and Problem-Solving Exercises - Page 170: 62

x is any rational or irrational number where x>0 y is any rational or irrational number where y=−x

For $x^2$ to equal $y^2$, the absolute values of x and y must be equal. Since it is given that x>y, x must be positive, and y must be negative and the opposite of x.