HMMT 2013 U2

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The real numbers $x, y, z$ satisfy $0 \leq x \leq y \leq z \leq 4$ . If their squares form an arithmetic progression with common difference 2 , determine the minimum possible value of $|x-y|+|y-z|$ .

Dataset text NuminaMath olympiads. Quoted with source.

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4-2 \sqrt{3}

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