Question 3
(GDR 1) Knowing that the system
$$\begin{cases}x+y+z=3,\\x^3+y^3+z^3=15,\\x^4+y^4+z^4=35,\end{cases}$$
has a real solution $x,y,z$ for which $x^2+y^2+z^2\lt 10$, find the value of $x^5+y^5+z^5$ for that solution.
$$\begin{cases}x+y+z=3,\\x^3+y^3+z^3=15,\\x^4+y^4+z^4=35,\end{cases}$$
has a real solution $x,y,z$ for which $x^2+y^2+z^2\lt 10$, find the value of $x^5+y^5+z^5$ for that solution.