PL-OM 2025 Problem 1

Find all $(a, b, c, d)\in \mathbb{R}$ satisfying $\begin{aligned} \begin{cases} a+b+c+d=0, a^2+b^2+c^2+d^2=12, abcd=-3. \end{cases} \end{aligned}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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