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sqrt[3]{Σa_i^3} \le \sqrt{Σ_i^2}

Source: Nordic Mathematical Contest 1990 #2

October 5, 2017
inequalitiespowers

Problem Statement

Let a1,a2,...,ana_1, a_2, . . . , a_n be real numbers. Prove a13+a23+...+an33≤a12+a22+...+an2\sqrt[3]{a_1^3+ a_2^3+ . . . + a_n^3} \le \sqrt{a_1^2+ a_2^2+ . . . + a_n^2} (1) When does equality hold in (1)?
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