Problem
TxO Math Bowl 2024 - Individuals B - Problem 10
Let x, y, z be rational numbers satisfying:
\begin{cases} x^3 + 6x^2y + 3x^2z + 9xyz = 152 \\ 2y^3 + 3xy^2 + 3y^2z = 20 \\ z^3 + 3xz^2 + 6yz^2 + 3xyz = 280 \end{cases}
Compute x + y + z.
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