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AUSTRIAN-POLISH 1989 Problem 1

    Show that (∑i=1nxiyizi)2≤(∑i=1nxi3)(∑i=1nyi3)(∑i=1nzi3)(\sum_{i=1}^{n}x_iy_iz_i)^2 \le (\sum_{i=1}^{n}x_i^3) (\sum_{i=1}^{n}y_i^3) (\sum_{i=1}^{n}z_i^3) for any positive reals xi,yi,zix_i, y_i, z_i .

    Dataset text AI-MO AoPS. Quoted with source.

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