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Romania NMO 2022 Grade 9 P1

Source: Romania National Olympiad 2022

April 21, 2022
algebraromania

Problem Statement

Let a,ba,b be positive integers. Prove that the equation x2+(a+b)2x+4ab=1x^2+(a+b)^2x+4ab=1 has rational solutions if and only if a=ba=b.
Mihai Opincariu
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