olymmath

ISL 2021 A4

    Show that for all real numbers x1,…,xnx_{1}, \ldots, x_{n} the following inequality holds: ∑i=1n∑j=1n∣xi−xj∣⩽∑i=1n∑j=1n∣xi+xj∣\sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{\left|x_{i}-x_{j}\right|} \leqslant \sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{\left|x_{i}+x_{j}\right|}

    Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

    Official text: IMO 2021 Shortlist booklet, page 5.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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