How Do We Systematically Substitute Them?

Algebra Level 3

P=a22a2+bc+b22b2+ca+c22c2+ab.P=\dfrac{a^2}{2a^2+bc}+\dfrac{b^2}{2b^2+ca}+\dfrac{c^2}{2c^2+ab}.

Let a,a, bb and cc be such that a+b+c=0a + b + c = 0.

Find the sum of all possible values of PP .

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