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ISL 1970 Problem 36

    Let x,y,zx, y, z be non-negative real numbers satisfying x2+y2+z2=5 and yz+zx+xy=2.x^2 + y^2 + z^2 = 5 \text{ and } yz + zx + xy = 2. Which values can the greatest of the numbers x2−yz,y2−xzx^2 -yz, y^2 - xz and z2−xyz^2 - xy have?

    Dataset text AI-MO AoPS. Quoted with source.

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