Inequality. Right?

Algebra Level 4

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

Let aa, bb and cc be real numbers satisfying a+b+c=0a + b + c = 0, find the value of PP such that PP is defined.

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