Maximum Value

Algebra Level pending

If a, b, c are real numbers and \(x \in \mathbb [1;3]\). Such that a + b + c = 6. Find the maximum value of P = \( \frac{a^{2} b^{2} + b^{2}c^{2} + c^{2}a^{2} +12abc +72} {ab + bc + ca} - \frac {1}{2} abc\)

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