DE-MO 2022 Problem 1
Determine all real numbers for which the system of equations \begin{align*} 3x^2+2y^2+2z^2&=a 4x^2+4y^2+5z^2&=1-a \end{align*} has at least one solution in the real numbers.
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
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