Weird inequality problem.

Algebra Level 5

Determine the least real number \(\xi\) such that the inequality

\[\left|ab(a^2-b^2)+bc(b^2-c^2)+ca(c^2-a^2)\right|\leqslant \xi(a^2+b^2+c^2)^2\]

holds for all real numbers \(a,b\) and \(c\).

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