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sum a^{11}/b^5c^5 >= a+b+c

Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p8 sl-12 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 14, 2022
inequalitiesalgebra

Problem Statement

Let a,b,c∈R+a,b,c\in\mathbb{R^+}. Prove that a11b5c5+b11c5a5+c11a5b5≥a+b+c\frac{a^{11}}{b^5c^5}+\frac{b^{11}}{ c^5a^5}+\frac{c^{11}}{a^5b^5}\ge a+b+c (Real Matrik)
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