Question 13
Initially, the number $1$ and two positive numbers $x$ and $y$ are written on a blackboard. In each move, a player may choose two numbers on the board, not necessarily distinct, and write their sum or their difference on the board. We may also choose a nonzero number on the board and write its reciprocal. After a finite number of moves, describe how we can obtain the following numbers:
a) $x^{2}$.
b) $x y$.
a) $x^{2}$.
b) $x y$.