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-

Tinku Tara June 4, 2023 None 0 Comments

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

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

$${Let}\:\:{a},\:{b},\:{c}\:\:\:{are}\:\:{positive}\:{real}\:\:{numbers}\:\:{such}\:\:{that}\:\:\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:\:=\:\:\mathrm{3}\:. \\ $$$${Prove}\:{that}\::\:\:\:{a}\:+\:{b}\:+\:{c}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\left({abc}\right)^{\mathrm{2}} }}\:\:\:\geqslant\:\:\mathrm{5} \\ $$

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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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