Find all solutions of the system $\sqrt[3]{\frac{yz^4}{x^2}}+2wx=0 $ $\sqrt[3]{\frac{xz^4}{y}}+5wy=0 $ $\sqrt[3]{\frac{xy}{x}}+7wz^{-1/3}=0$ $x^{12}+\frac{125}{4}y^5+\frac{343}{2}z^4=16$ where $x, y, z \ge 0$ and $w \in R$
HIDE: PS I attached the system, in case I have any typosAttachments:
