ab in terms of inverse and sum / differences of a,b
Source: 2004 Moldova JBMO TST p8
February 20, 2021
algebraProduct
Problem Statement
The positive real numbers and () are written on the board. At every step, with numbers written on the board, one of the following operations can be performed:
a) choose one of the numbers and write its square or its inverse.
b) choose two numbers written on the board ¸and write their sum or their positive difference.
Show how the product can be obtained with the help of the defined operations.