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Parametrized inequality

Source: Czech and Slovak Olympiad 1970, National Round, Problem 3

July 4, 2024
parameterizationalgebrarootsinequalities

Problem Statement

Let p>0p>0 be a given parameter. Determine all real xx such that 1 x+p−x2  +1 x−p−x2  ≥1 p .\frac{1}{\,x+\sqrt{p-x^2\,}\,}+\frac{1}{\,x-\sqrt{p-x^2\,}\,}\ge\frac{1}{\,p\,}.
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