The Integer Part of a Radical Sum

★ 7/10Convexity algebra Estimation inequality

Problem

Positive reals $a, b, c$ satisfy $a + b + c = 1$ . Find the integer part of

\sqrt{3a^2+1} + \sqrt{3b^2+1} + \sqrt{3c^2+1}.

Answer

Solution

Difficulty	7/10
Topics	Convexity, algebra, Estimation, inequality

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