Find the minimum

Algebra Level 5

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

Let a , b , c > 0 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 ( a b + b c + c a ) + a b c P=2(a^3+b^3+c^3)+4(ab+bc+ca)+abc


The answer is 19.

Mardokay Mosazghi by Mardokay Mosazghi , 22, USA

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