5

Part of 1997 India Regional Mathematical Olympiad

Problems(1)

These are lengths of sides

Source: Indian RMO 1997 Problem 5

x,y,z

be three distinct real positive numbers, Determine whether or not the three real numbers

\left| \frac{x}{y} - \frac{y}{x}\right| ,\left| \frac{y}{z} - \frac{z}{y}\right |, \left| \frac{z}{x} - \frac{x}{z}\right|

can be the lengths of the sides of a triangle.

inequalitiestriangle inequalityrearrangement inequality