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MathNet 2004 — Part 02 Question 73

Math Olympiad Vault · MathNet 2004 — Part 02

Question 73

to demonstrate inequality
$$
\frac{x+y}{x^{2}-x y+y^{2}} \leq \frac{2 \sqrt{2}}{\sqrt{x^{2}+y^{2}}}
$$
for any real numbers $x$ şi $y$, not simultaneously null.