olymmath

GR-HMS 2023 Problem 1

    Find all quadruplets (x, y, z, w) of positive real numbers that satisfy the following system: {xyz+1x+1=yzw+1y+1=zwx+1z+1=wxy+1w+1x+y+z+w=48\begin{cases} \frac{xyz+1}{x+1}= \frac{yzw+1}{y+1}= \frac{zwx+1}{z+1}= \frac{wxy+1}{w+1} x+y+z+w= 48 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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