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min {r-s^2,s-u^2, u-v^2,v-r^2 } <= 1/4

Source: 2005 Spanish Mathematical Olympiad P5

July 20, 2018

inequalitiesreal numbersminimum

Problem Statement

Let

r,s,u,v

be real numbers. Prove that:

min\{r-s^2,s-u^2, u-v^2,v-r^2\}\le \frac{1}{4}