Lowering the exponents

Algebra Level 3

\[ \large{\begin{cases}x^2+y^2=2 \\ x^3+y^3 = -2 \end{cases}} \]

If \(x\) and \(y\) are number satisfying the system of equations above, find the value(s) of \(x+y\).

(A): \(-2\)
(B): \(1 +\sqrt3\)
(C): \(1 -\sqrt3\)

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