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These are lengths of sides

Source: Indian RMO 1997 Problem 5

October 26, 2005
inequalitiestriangle inequalityrearrangement inequality

Problem Statement

Let x,y,zx,y,z be three distinct real positive numbers, Determine whether or not the three real numbers ∣xy−yx∣,∣yz−zy∣,∣zx−xz∣ \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.
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