olymmath

BxMO 2018 Problem 1

    (a) Determine the minimal value of

    (x+1y)(x+1y−2018)+(y+1x)(y+1x−2018)\left(x+\frac{1}{y}\right)\left(x+\frac{1}{y}-2018\right)+\left(y+\frac{1}{x}\right)\left(y+\frac{1}{x}-2018\right)

    where xx and yy vary over the positive reals. (b) Determine the minimal value of

    (x+1y)(x+1y+2018)+(y+1x)(y+1x+2018)\left(x+\frac{1}{y}\right)\left(x+\frac{1}{y}+2018\right)+\left(y+\frac{1}{x}\right)\left(y+\frac{1}{x}+2018\right)

    where xx and yy vary over the positive reals. (Pierre Haas, Luxembourg)

    Dataset text NuminaMath olympiads. Quoted with source.

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