If a , b , c >0 , such that a+b+c=3 prove that (1/(1+ab))+(1/(1+ac))+(1/(1+bc))≥(9/(2((√a)+(√b)+(√c))))


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Question Number 194448 by York12 last updated on 07/Jul/23

$I f a, b, c > 0, s u c h t h a t a + b + c = 3$ $p r o v e t h a t$ $\frac{1}{1 + a b} + \frac{1}{1 + a c} + \frac{1}{1 + b c} ⩾ \frac{9}{2 (\sqrt{a} + \sqrt{b} + \sqrt{c})}$
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