# System of a zero

Algebra Level 4

$\large \begin{cases} \dfrac{x^4}{2x+yz} + \dfrac{y^4}{2y+zx} + \dfrac{z^4}{2z+xy} = 1 \\ & \\ x+y+z = 0 \end{cases}$

Let $$x,y$$ and $$z$$ be real numbers satisfying the system of equations above, where $$2x+yz \ne 0$$, $$2y+zx \ne 0$$ and $$2z+xy \ne 0$$.

Find the value of $$x^4+y^4+z^4$$.

×

Problem Loading...

Note Loading...

Set Loading...