olymmath

IMO 2021 Problem 2

  • Day 1

Show that the inequality ∑i=1n∑j=1n∣xi−xj∣⩽∑i=1n∑j=1n∣xi+xj∣\sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i-x_j|}\leqslant \sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i+x_j|}holds for all real numbers x1,…xn.x_1,\ldots x_n.

Official text Transcription from AI-MO AoPS, checked word for word against the official paper. Quoted with source.

Official text: IMO 2021 official English paper, page 1.

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