IMO Shortlist 1971 problem 3


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Dodao/la: arhiva
April 2, 2012
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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.
Source: Međunarodna matematička olimpijada, shortlist 1971