Khang's inequality

Algebra Level 5

Suppose \(a, b, c\) are non-negative real numbers with \(a+b+c=3\).

Find the maximum value of:

\[\large P=\dfrac{1}{a+1}+\dfrac{1}{b+1}+\dfrac{1}{c+1}-\dfrac{1}{\sqrt[5]{ab+bc+ca}}\]

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