Simultaneous Equations

Algebra Level 5

Given the following simultaneous equations, determine the product \(abc\).

\(a^3 + 11(b^2 + c^2) + 36a = 575,\)
\(b^3 + 11(c^2 + a^2) + 36b = 575,\)
\(c^3 + 11(a^2 + b^2) + 36c = 575.\)

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