IMO Shortlist 1971 problem 3
Dodao/la:
arhiva2. travnja 2012. Knowing that the system
![x^4 + y^4 + z^4 = 35,](/media/m/1/d/0/1d0866e324dbbab58439d658eb58ad53.png)
has a real solution
![x, y, z](/media/m/e/1/6/e160f3439547ca8c1afcc35a1c26f080.png)
for which
![x^2 + y^2 + z^2 < 10](/media/m/d/1/c/d1cb96c40b246ece9b8439771c2c3427.png)
, find the value of
![x^5 + y^5 + z^5](/media/m/9/d/d/9dd9612f6be30c3daa70cb24dcb022ab.png)
for that solution.
%V0
Knowing that the system
$$x + y + z = 3,$$ $$x^3 + y^3 + z^3 = 15,$$ $$x^4 + y^4 + z^4 = 35,$$
has a real solution $x, y, z$ for which $x^2 + y^2 + z^2 < 10$, find the value of $x^5 + y^5 + z^5$ for that solution.
Izvor: Međunarodna matematička olimpijada, shortlist 1971