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Romania NMO 2022 Grade 9 P4

Source: Romania National Olympiad 2022

April 21, 2022
romaniaalgebrainequalities

Problem Statement

Let a<b<c<da<b<c<d be positive integers which satisfy ad=bc.ad=bc. Prove that 2a+a+d<b+c+1.2a+\sqrt{a}+\sqrt{d}<b+c+1.
Marius Mînea
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