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1/(x+y)^2+1/x^2+1/y^2>=9/4xy (VI Soros Olympiad 1990-00 R1 8.7)

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May 27, 2024

algebrainequalities

Problem Statement

Prove that for any positive real

x

and

y

, holds the inequality

\frac{1}{(x+y)^2}+\frac{1}{x^2}+\frac{1}{y^2} \ge \frac{9}{4xy}