CZ-SK-MO 1991 Problem 1

Prove that for any real numbers $p,q,r,\phi$ ,: $\cos^2\phi+q \sin \phi \cos \phi +r\sin^2 \phi \ge \frac12 (p+r-\sqrt{(p-r)^2+q^2})$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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