Problem
ALG-B2-M12-P012 Set 3. Five numbers
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Five real numbers differ pairwise by at least \(d>0\), and their sum is \(0\). Prove that the sum of their squares is at least \(10d^2\).
Hint. Order the numbers and use the sum of squared pairwise differences.
Let \(y_1<\cdots
Mock set 3: the problem is intended for independent method selection without an explicit cue in the statement.