Let a, b, c are positive real numbers such that (1/a) + (1/b) + (1/c) = 3 . Prove that : a + b + c + (4/(1 + (((abc)^2 ))^(1/3) )) ≥ 5


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Question Number 33681 by naka3546 last updated on 22/Apr/18

$L e t a, b, c a r e p o s i t i v e r e a l n u m b e r s s u c h t h a t \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 3 .$ $P r o v e t h a t : a + b + c + \frac{4}{1 + \sqrt[3]{{(a b c)}^{2}}} ⩾ 5$
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