If-a-b-c-gt-0-such-that-a-b-c-3-prove-that-1-1-ab-1-1-ac-1-1-bc-9-2-a-b-c-

Question Number 194421 by York12 last updated on 06/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})}

Commented 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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