# Find the minimum

Algebra Level 5

$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\le\frac{a+b+c}{2}$

Let $$a,b,c >0$$ satisfying the inequality above.

Find the minimum value of the expression below. $P=2(a^3+b^3+c^3)+4(ab+bc+ca)+abc$

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