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| x_1x_4-x_1x_5 +x_2x_5 -x_2x_6+x_3x_6-x_3x_4| >= 4M^2

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1982 p2

September 10, 2024
algebrainequalities

Problem Statement

Given real numbers x1x_1, x2x_2, x3x_3, x4x_4, x5x_5, x6x_6. Let MM denote the maximum of their absolute values. Prove that it is valid ∣x1x4−x1x5+x2x5−x2x6+x3x6−x3x4∣≤4M2 | x_1x_4-x_1x_5 +x_2x_5 -x_2x_6+x_3x_6-x_3x_4| \le 4M^2
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