Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.5 National olympiad Prove it

45. Given that $a, b, c$ are positive real numbers, and satisfy $a b c=1$ , prove: $\frac{1}{a^{5}(b+2 c)^{2}}+\frac{1}{b^{5}(c+2 a)^{2}}+$ $\frac{1}{c^{5}(a+2 b)^{2}} \geqslant \frac{1}{3} \cdot(2010$ USA Training Team Problem)

Solution

None

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