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Moldova TST, easy inequality

Source: Moldova TST 2014, First Day, Problem 2

March 4, 2014
inequalitiesinequalities proposed

Problem Statement

Let a,b∈R+a,b\in\mathbb{R}_+ such that a+b=1a+b=1. Find the minimum value of the following expression:
E(a,b)=31+2a2+240+9b2.E(a,b)=3\sqrt{1+2a^2}+2\sqrt{40+9b^2}.
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