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#1 2012-09-18 23:57:47

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,404
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What must be added?

What must be added to the following expression to make it a perfect square?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2012-09-19 01:22:18

Sylvia104
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Registered: 2011-09-19
Posts: 26

Re: What must be added?

Let
.

Expanding,

.

Comparing coefficients gives

.

Hence you must add

:

Last edited by Sylvia104 (2012-09-19 01:23:29)

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#3 2012-09-19 03:44:13

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,404
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Re: What must be added?

Please expain why you get

Last edited by Agnishom (2012-09-19 03:45:47)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2012-09-19 04:14:07

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,404
Website

Re: What must be added?

Yeah!
I coudn't pay enough concentration.
sad
Sometimes it happens


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#5 2012-09-19 05:30:31

Au101
Member
Registered: 2010-12-01
Posts: 270

Re: What must be added?

Hi smile

Last edited by Au101 (2012-09-19 05:31:13)

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#6 2012-09-19 17:01:09

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,404
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Re: What must be added?

Thanks!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#7 2012-09-19 19:01:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: What must be added?

Hi Agnishom;

There is another way which does not require any of the heavy machinery.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8 2012-09-21 00:57:49

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,404
Website

Re: What must be added?

Really? Whazzit?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#9 2012-09-21 01:04:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: What must be added?

Hi;

The method depends on inspection and some knowledge of common squares. I am only offering it as a sometime faster alternative. In most cases you should use and learn the method used in post #2.

Let b be what you have to add.

You are looking for a b in

that makes a square. So start with

You have 2 equations which say what b must be added to b + 56 and b + 200 that give you two squares. Well the next square after 56 is 64 so b = 8 is a possibility but 200 + 8 is not a square.

Then next square is 81 which means in b + 56 = 81 b would be 25. Plugging in b into the second equation 25 + 200 = 225 which is a square too. You are done, b = 25.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#10 2012-09-21 16:16:19

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,404
Website

Re: What must be added?

I think #2 was better hmm
It doesn't look very tedious except that I was a little bit confused then


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#11 2012-09-21 19:20:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: What must be added?

Okay, I just thought you might want to see something else.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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