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Easy equation with a parametr

Source: Czech and Slovak Olympiad 1957, National Round, Problem 1

April 10, 2020
equationparametric equationalgebranational olympiadparameterization

Problem Statement

Find all real numbers pp such that the equation x2−5p2=px−1\sqrt{x^2-5p^2}=px-1 has a root x=3x=3. Then, solve the equation for the determined values of pp.
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