Weird inequality problem.

Algebra Level 5

Determine the least real number ξ\xi such that the inequality

ab(a2b2)+bc(b2c2)+ca(c2a2)ξ(a2+b2+c2)2\left|ab(a^2-b^2)+bc(b^2-c^2)+ca(c^2-a^2)\right|\leqslant \xi(a^2+b^2+c^2)^2

holds for all real numbers a,ba,b and cc.

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