Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.1 National olympiad Prove it

83. Given $a, b, c > 0$ , and $\frac{1}{a+b+1}+\frac{1}{b+c+1}+\frac{1}{c+a+1} \geqslant 1$ , prove: $a+b+$ $c \geqslant a b+b c+c a$ . (2007 Junior Balkan Mathematical Olympiad)

Solution

None

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