Let $a$, $b$ and $c$ be positive real numbers such that $abc = 1$. Prove that $$\displaystyle \sum_{cyc} \sqrt{\frac{a}{a+8}} \geq 1.$$
I have tried using some substitutions but still cannot do it. Please suggest.
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Martin Sleziak
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user403160
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I don't think that it's not so duplicate because at least one of my solutions different than solution in the linked topic. – Michael Rozenberg Jul 19 '17 at 05:42
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@MichaelRozenberg BTW by using (at)Martin instead of (at)MartinR you pinged me - my guess is that this was not what you intended. I think that you have participated in a few discussions about duplicates - so you already know that closing a post as a duplicated does not delete the answers. – Martin Sleziak Jul 19 '17 at 08:13
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@Martin Sleziak See here https://math.stackexchange.com/questions/2347703 With duplicates sometimes happens the similar thing. I'll get an example. I did not ping you. Why do you speak to me with this tone? – Michael Rozenberg Jul 19 '17 at 08:17