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 \(a \times b \times c\)?
by
Ajay Dutta