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3

Part of 1965 Czech and Slovak Olympiad III A

Problems(1)

Parametrized radicals

Source: Czech and Slovak Olympiad 1965, National Round, Problem 3

6/25/2024
Find all real roots xx of the equation x2−2x−1+x2+2x−1=p,\sqrt{x^2-2x-1}+\sqrt{x^2+2x-1}=p, where pp is a real parameter.
algebraReal Rootsparameterradicalequation