# System of Cubic Equations

**Algebra**Level 5

**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 \(a \times b \times c\)?

**Your answer seems reasonable.**Find out if you're right!

Sign up to access problem solutions.

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.