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Interesting inequality

Source: EGMO 2018 Moldova TST - Mongolia National Math Olympiad 2017, Grade 9, Problem 4

February 11, 2018
inequalities

Problem Statement

Let aa and bb be real numbers such that a+b=1a + b = 1. Prove the inequality 1+5a2+52+b2≥9.\sqrt{1+5a^2} + 5\sqrt{2+b^2} \geq 9.
Proposed by Baasanjav Battsengel
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