Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.4 National olympiad Prove it

68. (Original problem, 2006.08.31) Let $x, y, z, u, v \in \mathbf{R}^{+}$ , and $3(u+v) x y z \geqslant$ $u \sum x^{2}+v \sum y z$ , then
$(57 u+9 v) \sum x \leqslant 3(11 u+3 v) \sum y z+72 u$

Equality holds if and only if $x=y=z=1$ .

Solution

None

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