Polynomial Again?

Algebra Level 5

{x3xyz=2y3xyz=6z3xyz=20 \begin{cases} x^3-xyz=2 \\ y^3-xyz =6 \\ z^3-xyz = 20 \end{cases}

If x,yx,y and zz are real solutions satisfying the system of equations above, and the maximum value of x3+y3+z3x^3+y^3+z^3 is equal to mn \dfrac mn, where mm and nn are coprime positive integers, find m+nm+n.

×

Problem Loading...

Note Loading...

Set Loading...