Power sums of a,b,c,d,e in [-2,2]
Source: Romanian MO 2002
December 8, 2010
trigonometryalgebra proposedalgebra
Problem Statement
Find all real numbers in the interval , that satisfy:
\begin{align*}a+b+c+d+e &= 0\\ a^3+b^3+c^3+d^3+e^3&= 0\\ a^5+b^5+c^5+d^5+e^5&=10 \end{align*}