How Do We Systematically Substitute Them?

Algebra Level 3

\[P=\dfrac{a^2}{2a^2+bc}+\dfrac{b^2}{2b^2+ca}+\dfrac{c^2}{2c^2+ab}.\]

Let \(a,\) \(b\) and \(c\) be such that \(a + b + c = 0\).

Find the sum of all possible values of \(P \).

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