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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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**Sylvia104****Member**- Registered: 2011-09-19
- Posts: 26

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)*

'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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Yeah!

I coudn't pay enough concentration.

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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**Au101****Member**- Registered: 2010-12-01
- Posts: 286

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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Really? Whazzit?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

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

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

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