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Muirhead's does not work here...

Prove that

\( \sum_{\text{sym}} 3a^4+7b^2c^2 \ge \sum_{\text{sym}} 7a^3b \)

for positive \( a, b, c \)

Note by Kaan Dokmeci
3 years, 6 months ago

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I've been wondering whether or not I should use Muirhead at Olympiads, the same goes for Lagrange multipliers, are these viable? Of course, only if I do not see the beautiful classic inequality solution.

Adrian Stefan - 3 years, 6 months ago

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An inequality that is true by Muirhead can be shown by a clever application of weighted AM-GM.

Lagrange Multipliers can be used but you have to be rigorous about everything, or points will be fiercely deducted.

Kaan Dokmeci - 3 years, 6 months ago

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As a hint I found this by playing around with certain expansions, namely squares.

Kaan Dokmeci - 3 years, 6 months ago

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