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|a - b| = 2|b -c| = 3|c - d| = 4|d- e| = 5|e - a| 2009 Romania District VIII p2

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August 16, 2024
algebrasystem of equations

Problem Statement

Real numbers a,b,c,d,ea, b, c, d, e, have the property ∣a−b∣=2∣b−c∣=3∣c−d∣=4∣d−e∣=5∣e−a∣.|a - b| = 2|b -c| = 3|c - d| = 4|d- e| = 5|e - a|. Prove they are all equal.
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