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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**Sylvia104****Banned**- Registered: 2011-09-19
- Posts: 29

Let .

Expanding,

.Comparing coefficients gives

.Hence you must add

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

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Please expain why you get

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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Yeah!

I coudn't pay enough concentration.

Sometimes it happens

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**Au101****Member**- Registered: 2010-12-01
- Posts: 351

Hi

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

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Thanks!

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,917

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.**

**If it ain't broke, fix it until it is.**

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Really? Whazzit?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,917

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.**

**If it ain't broke, fix it until it is.**

**Online**

I think #2 was better

It doesn't look very tedious except that I was a little bit confused then

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,917

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

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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