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Note by Saran Balachandar 2 years, 5 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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Using the first equation and AM - GM inequality, we have

\( \frac{a+b}{2} \geq \sqrt{ab} \)

\( 4 \geq ab \)

From the second eq.

\( c^2 - 2\sqrt{3}c + 3 = \frac{ab}{2}- 2 \)

\( (c - \sqrt{3})^2 = \frac{ab}{2} - 2 \)

Since the left side is a square and thus positive, the right side must be positive, that is we must have \( \frac{ab}{2} \geq 2 \implies ab \geq 4 \)

Therefore, we see that \( ab = 4 \). Which implies \( a = b = 2 \) and \( c = \sqrt{3} \)

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Comment deleted Oct 03, 2016

Try the wiki.

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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

Sort by:

TopNewestUsing the first equation and AM - GM inequality, we have

\( \frac{a+b}{2} \geq \sqrt{ab} \)

\( 4 \geq ab \)

From the second eq.

\( c^2 - 2\sqrt{3}c + 3 = \frac{ab}{2}- 2 \)

\( (c - \sqrt{3})^2 = \frac{ab}{2} - 2 \)

Since the left side is a square and thus positive, the right side must be positive, that is we must have \( \frac{ab}{2} \geq 2 \implies ab \geq 4 \)

Therefore, we see that \( ab = 4 \). Which implies \( a = b = 2 \) and \( c = \sqrt{3} \)

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Comment deleted Oct 03, 2016

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Try the wiki.

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