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Problem 2 -- Square Dancing Inequality

Source: 47th Austrian Mathematical Olympiad Beginners' Competition Problem 2

July 27, 2018
Austriainequalitiesalgebra

Problem Statement

Prove that all real numbers x≠−1x \ne -1, y≠−1y \ne -1 with xy=1xy = 1 satisfy the following inequality:
(2+x1+x)2+(2+y1+y)2≥92\left(\frac{2+x}{1+x}\right)^2 + \left(\frac{2+y}{1+y}\right)^2 \ge \frac92
(Karl Czakler)
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