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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'

I'm not crazy, my mother had me tested.

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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'

I'm not crazy, my mother had me tested.

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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'

I'm not crazy, my mother had me tested.

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**Au101****Member**- Registered: 2010-12-01
- Posts: 353

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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,294

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.****No great discovery was ever made without a bold guess. **

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Really? Whazzit?

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,294

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.****No great discovery was ever made without a bold guess. **

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,294

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.****No great discovery was ever made without a bold guess. **

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