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a + b + c =? when a^2 + b^2 + c^2 = 1, a^3 + b^3 + c^3 = 1

Source: 2004 Estonia National Olympiad Final Round grade 10 p5

March 25, 2020
algebrasystem of equations

Problem Statement

Real numbers a,ba, b and cc satisfy {a2+b2+c2=1a3+b3+c3=1.\begin{cases} a^2 + b^2 + c^2 = 1 \\ a^3 + b^3 + c^3 = 1. \end{cases} Find a+b+ca + b + c.
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