Problem
ALG-B2-M12-P020 Set 5. Six separated numbers
#20
★★★★★ Level 5 of 5
Six real numbers differ pairwise by at least \(d>0\), and their sum is \(0\). Prove that the sum of their squares is at least \(\frac{35}{2}d^2\).
Hint. Order the numbers and compute \(\sum_{i
Let \(y_1<\cdots
Mock set 5: the problem is intended for independent method selection without an explicit cue in the statement.