Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.2 National olympiad Prove it

28. Given $a, b, c>0$ , prove: $\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c} \geqslant$ $\frac{\left(a^{2}+b^{2}+c^{2}\right)(a b+b c+c a)}{a b c(a+b+c)} \cdot(2006$ Romanian Mathematical Olympiad problem)

Solution

None

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