Cubic equation in three variables

Algebra Level 2

x+y+z=4x2+y2+z2=14x3+y3+z3=34\begin{aligned} x + y + z &=& 4 \\ x^{2} + y^{2} + z^{2} &=& 14 \\ x^{3} + y^{3} + z^{3} &=& 34 \\ \end{aligned}

There are many different sets of solutions to the above system of equations.

Let SS be the sum of all possible values of xx. Find SS.

×

Problem Loading...

Note Loading...

Set Loading...