Problem #PRU-65558

Problems Algebra Mean values Methods Pigeonhole principle Pigeonhole principle (other)

Problem

Harry thought of two positive numbers \(x\) and \(y\). He wrote down the numbers \(x + y\), \(x - y\), \(xy\) and \(x/y\) on a board and showed them to Sam, but did not say which number corresponded to which operation.

Prove that Sam can uniquely figure out \(x\) and \(y\).