# Two Symmetric Equations

Algebra Level 3

If $$a, b$$ and $$c$$ are non-zero real numbers, that satisfy the equations $$a^2 + b^2 + c^2 = 1$$ and $$a\left(\frac {1}{b} + \frac {1}{c}\right) + b\left(\frac {1}{c} + \frac {1}{a}\right) + c\left( \frac {1}{a} + \frac {1}{b}\right) = -3$$, how many possible values are there for $$a + b + c$$?

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