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Inequality of six variables (easy)

Source: Bogdan Stan 2011

October 7, 2019
inequalitiescauchy schwarz

Problem Statement

Prove that a+b+c>(α+β+γ)2, a+b+c>\left( \sqrt\alpha +\sqrt\beta +\sqrt\gamma \right)^2, for all positive real numbers a,b,c,α,β,γ a,b,c,\alpha ,\beta ,\gamma that are under the condition abc>αbc+βac+γab. abc>\alpha bc+\beta ac+\gamma ab.
Țuțescu Lucian and Chiriță Aurel
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