New user? Sign up

Existing user? Log in

We have a,b,c>0. Prove (a+b/ac)(b+c/ab)(c+a/bc)>=8 Please help me. Thanks.

Note by Hermione Taylor 5 years 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}

Sort by:

Using AM-GM inequality, a+(b/ac)>2(b/c) , b+(c/ab)>2c/a , c+(a/bc)>2a/b, Multiplying these expressions you would automatically get the result.

Log in to reply

You're wrong, but the principle is right. \(a+\frac{b}{ac} \geq 2\sqrt{\frac{b}{c}}\). You just forgot the square root. But when you multiply them together, they cancel anyways, leaving a 1 under the square root.

Actually I entered the square root but it was not displayed in the answer, don't know why.

@Siddharth Kumar – Weird. Oh well. It works anyways.

Get it. Thank you very much

help me plz we have ab+bc+ca=0 calculate (a+b/c)+(b+c/a)+(c+a/b)

Problem Loading...

Note Loading...

Set Loading...

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 AM-GM inequality, a+(b/ac)>2(b/c) , b+(c/ab)>2c/a , c+(a/bc)>2a/b, Multiplying these expressions you would automatically get the result.

Log in to reply

You're wrong, but the principle is right. \(a+\frac{b}{ac} \geq 2\sqrt{\frac{b}{c}}\). You just forgot the square root. But when you multiply them together, they cancel anyways, leaving a 1 under the square root.

Log in to reply

Actually I entered the square root but it was not displayed in the answer, don't know why.

Log in to reply

Log in to reply

Get it. Thank you very much

Log in to reply

help me plz we have ab+bc+ca=0 calculate (a+b/c)+(b+c/a)+(c+a/b)

Log in to reply