System of Cubic Equations

Algebra Level 5

If distinct real numbers aa, bb and cc satisfy the system of equations a33a2+2a33=a2+b2+c2,b33b2+2b33=a2+b2+c2,c33c2+2c33=a2+b2+c2,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×b×ca \times b \times c?

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