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Determine the least real number ξ\xiξ such that the inequality
∣ab(a2−b2)+bc(b2−c2)+ca(c2−a2)∣⩽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∣∣ab(a2−b2)+bc(b2−c2)+ca(c2−a2)∣∣⩽ξ(a2+b2+c2)2
holds for all real numbers a,ba,ba,b and ccc.
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