IMO Shortlist 2016 problem A1


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Dodao/la: arhiva
3. listopada 2019.
2016 alg nejednakost shortlist
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Let a, b, c be positive real numbers such that \min(ab,bc,ca) \ge 1. Prove that \sqrt[3]{(a^2+1)(b^2+1)(c^2+1)} \le \left(\frac{a+b+c}{3}\right)^2 + 1.

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf