Real numbers $a, b$ and $c$ satisfy $$\begin{cases} a^2 + b^2 + c^2 = 1 \\ a^3 + b^3 + c^3 = 1. \end{cases}$$Find $a + b + c$.
Problem
Source: 2004 Estonia National Olympiad Final Round grade 10 p5
Tags: algebra, system of equations
Source: 2004 Estonia National Olympiad Final Round grade 10 p5
Tags: algebra, system of equations
Real numbers $a, b$ and $c$ satisfy $$\begin{cases} a^2 + b^2 + c^2 = 1 \\ a^3 + b^3 + c^3 = 1. \end{cases}$$Find $a + b + c$.