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Inequality - 2015 PAMO Problem 1

Source: 2015 Pan-African Mathematics Olympiad Problem 1

August 26, 2015
inequalities

Problem Statement

Prove that x−1+2x+9+19−3x<9\sqrt{x-1}+\sqrt{2x+9}+\sqrt{19-3x}<9 for all real xx for which the left-hand side is well defined.
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