Menu Close

If-a-b-c-gt-0-and-abc-1-Prove-that-a-b-c-1-a-1-b-1-b-1-c-1-c-1-a-




Question Number 205640 by hardmath last updated on 26/Mar/24
If  a,b,c>0  and  abc≥1  Prove that:  a + b + c ≥ ((1+a)/(1+b)) + ((1+b)/(1+c)) + ((1+c)/(1+a))
$$\mathrm{If}\:\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{abc}\geqslant\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\geqslant\:\frac{\mathrm{1}+\mathrm{a}}{\mathrm{1}+\mathrm{b}}\:+\:\frac{\mathrm{1}+\mathrm{b}}{\mathrm{1}+\mathrm{c}}\:+\:\frac{\mathrm{1}+\mathrm{c}}{\mathrm{1}+\mathrm{a}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *