How to solve this system of equations? I tried to add and substract first and second equation but without any result.
$$ \begin{cases} \dfrac{x}{y} + \dfrac{y}{z} + \dfrac{z}{x} = 3\\ \dfrac{y}{x} + \dfrac{z}{y} + \dfrac{x}{z} = 3\\ x + y + z = 3 \\ \end{cases} $$
HINT :
Setting $\frac xy=a,\frac yz=b,\frac zx=c$ gives $$abc=1$$ $$a+b+c=3$$ $$\frac 1a+\frac 1b+\frac 1c=3\iff ab+bc+ca=3$$ So, $a,b,c$ are the roots of $X^3-3X^2+3X-1=0$.