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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, 11 months ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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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.

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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.

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

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestI'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.

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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.

Log in to reply

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

Log in to reply