IMO Shortlist 1959 problem 3


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2. travnja 2012.
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Let a,b,c be real numbers. Consider the quadratic equation in \cos{x} a \cos^2{x}+b \cos{x}+c=0. Using the numbers a,b,c form a quadratic equation in \cos{2x} whose roots are the same as those of the original equation. Compare the equation in \cos{x} and \cos{2x} for a=4, b=2, c=-1.
Izvor: Međunarodna matematička olimpijada, shortlist 1959