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Find $ab + bc + ca$ given that:

$a^{2} + ab + b^{2} = 2$

$b^{2} + bc + c^{2} = 1$

$c^{2} + ca + a^{2} = 3$

Giveb that a, b, and c are positive numbers.

Note by Christian Daang 3 years, 9 months ago

$</code> ... <code>$</code>...<code>."> Easy Math Editor

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# 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

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Is the question correct? There don't exist positive $a,b,c$ for which these equations are true.

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Yes sir, there is. :)

Christian Daang has posted the same problem recently.

Here

Yah sir, after a year and a half, I figure it out how this can be solve. :)

Its absolutely brilliant that you have devised your own method...:) :) :)

Please don't call me sir , I am your fellow BRILLIANTIAN and a FRIEND.

@Ankit Kumar Jain – I saw someone who figure it out how this can be solve. :) I just somewhat get it. XD And somewhat make it more elaborative.

~ Do you think there are other ways to solve this except for the geometric method?

@Christian Daang – At present , I can't think of any other way.

By the way , you post some really interesting questions ...I love them.

Even you can try my sets out

My Problems and THRILLER

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$</code> ... <code>$</code>...<code>."> 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 $</span> ... <span>$ or $</span> ... <span>$ 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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TopNewestIs the question correct? There don't exist positive $a,b,c$ for which these equations are true.

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Yes sir, there is. :)

Log in to reply

Christian Daang has posted the same problem recently.

Here

Log in to reply

Yah sir, after a year and a half, I figure it out how this can be solve. :)

Log in to reply

Its absolutely brilliant that you have devised your own method...:) :) :)

Please don't call me sir , I am your fellow BRILLIANTIAN and a FRIEND.

Log in to reply

~ Do you think there are other ways to solve this except for the geometric method?

Log in to reply

Log in to reply

By the way , you post some really interesting questions ...I love them.

Even you can try my sets out

My Problems and THRILLER

Log in to reply