MathDB

Let

(a,b,c)

be the real solution of the system of equations x^3 \minus{} xyz \equal{} 2, y^3 \minus{} xyz \equal{} 6, z^3 \minus{} xyz \equal{} 20. The greatest possible value of a^3 \plus{} b^3 \plus{} c^3 can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find m \plus{} n.

Problem Statement