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RU-ALLRUSSIAN 1984 Problem 12

    The positive reals x, y, z satisfy x2+xy+y2/3=25\mathrm{x^2 + xy + y^2 / 3 = 25} , y2/3+z2=9\mathrm{y^2 / 3 + z^2 = 9} , z2+zx+x2=16\mathrm{z^2 + zx + x^2 = 16} . Find the value of xy+2yz+3zx\mathrm{xy + 2yz + 3zx} .

    Dataset text NuminaMath olympiads. Quoted with source.

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