MathDB

8.7

Part of VI Soros Olympiad 1999 - 2000 (Russia)

Problems(1)

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

Source:

5/27/2024
Prove that for any positive real xx and yy, holds the inequality 1(x+y)2+1x2+1y2≥94xy\frac{1}{(x+y)^2}+\frac{1}{x^2}+\frac{1}{y^2} \ge \frac{9}{4xy}
algebrainequalities