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DE-MO 2000 Problem 4

    Find all nonnegative solutions (x,y,z)(x,y,z) to the system {x+y+z=7x+z+y=7y+z+x=5\begin{cases} \sqrt{x+y}+\sqrt{z} = 7 \sqrt{x+z}+\sqrt{y} = 7 \sqrt{y+z}+\sqrt{x} = 5 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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