MEMO 2017 ekipno problem 2


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12. rujna 2018.
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Determine the smallest possible real constant C such that the inequality |x^3 + y^3 + z^3 + 1| \leqslant C|x^5 + y^5 + z^5 + 1|holds for all real numbers x, y, z satisfying x + y + z = -1.

Izvor: Srednjoeuropska matematička olimpijada 2017, ekipno natjecanje, problem 2