HMMT 2005 A3

Let $x, y$ , and $z$ be distinct real numbers that sum to 0 . Find the maximum possible value of

$\frac{x y+y z+z x}{x^{2}+y^{2}+z^{2}} .$

Dataset text NuminaMath olympiads. Quoted with source.

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-\frac{1}{2}

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