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If-a-b-c-gt-0-and-abc-1-Then-a-b-2024-b-c-2024-c-a-2024-a-b-c-




Question Number 205421 by hardmath last updated on 20/Mar/24
If  a,b,c>0   and   abc=1  Then:  (a/b^(2024) ) + (b/c^(2024) ) + (c/a^(2024) ) ≥ a + b + c
$$\mathrm{If} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}=\mathrm{1} \\ $$$$\mathrm{Then}: \\ $$$$\frac{\mathrm{a}}{\mathrm{b}^{\mathrm{2024}} }\:+\:\frac{\mathrm{b}}{\mathrm{c}^{\mathrm{2024}} }\:+\:\frac{\mathrm{c}}{\mathrm{a}^{\mathrm{2024}} }\:\geqslant\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c} \\ $$

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