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Maestro composed an algebra so good we used it in two grades!

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 9.5, 10.5

March 20, 2024
algebraInequalityinequalities proposedinequalities

Problem Statement

For real numbers a,b,c,d∈[0,1]a, b, c, d \in [0, 1], find the largest possible value of the following expression:
a2+b2+c2+d2−ab−bc−cd−daa^2+b^2+c^2+d^2-ab-bc-cd-da
Proposed by Mykhailo Shtandenko
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