olymmath

BG-MO 2001 Problem 2

    Find all real values tt for which there exist real numbers xx , yy , zz satisfying : 3x2+3xz+z2=13x^2 + 3xz + z^2 = 1 , 3y2+3yz+z2=43y^2 + 3yz + z^2 = 4 , x2−xy+y2=tx^2 - xy + y^2 = t .

    Dataset text AI-MO AoPS. Quoted with source.

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