Let-a-b-c-gt-0-and-a-b-c-3-Prove-that-ab-1-ab-c-bc-1-bc-a-ca-1-ca-b-a-b-c-

Question Number 144118 by loveineq last updated on 21/Jun/21

Let a, b, c > 0 and a + b + c = 3 . Prove that

\frac{\sqrt{a b} + 1}{\sqrt{a b} + \sqrt{c}} + \frac{\sqrt{b c} + 1}{\sqrt{b c} + \sqrt{a}} + \frac{\sqrt{c a} + 1}{\sqrt{c a} + \sqrt{b}} ⩾ \sqrt{a} + \sqrt{b} + \sqrt{c}