Inequality. Right?

Algebra Level 4

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

Let \(a\), \(b\) and \(c\) be real numbers satisfying \(a + b + c = 0\), find the value of \(P\) such that \(P \) is defined.

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