Problem

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

Tags: algebra, Inequality, inequalities proposed, inequalities



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