# System of Cubic Equations

Algebra Level 5

If distinct real numbers $a$, $b$ and $c$ satisfy the system of equations $a^3-3a^2 +2a-33=a^2+b^2+c^2,\\ b^3-3b^2+2b-33=a^2+b^2+c^2,\\ c^3-3c^2+2c-33=a^2+b^2+c^2,$ what is the value of $a \times b \times c$?

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