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DK-GEORGMOHR 2000 Problem 5

    Determine all possible values of x+1xx+\frac{1}{x} , where the real number xx satisfies the equation x4+5x3−4x2+5x+1=0x^4+5x^3-4x^2+5x+1=0 and solve this equation.

    Dataset text AI-MO AoPS. Quoted with source.

    Official text: Georg Mohr Contest 2000 official paper, page 1.

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