Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.5 National olympiad Prove it

92. Given that $a, b, c$ are positive numbers, and $a b+b c+c a \leqslant 3 a b c$ , prove: $\sqrt{\frac{a^{2}+b^{2}}{a+b}}+$
$\sqrt{\frac{b^{2}+c^{2}}{b+c}}+\sqrt{\frac{c^{2}+a^{2}}{c+a}}+3 \leqslant \sqrt{2(a+b)}+\sqrt{2(b+c)}+\sqrt{2(c+a)} \cdot \text { (2009)}$

Solution

None

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