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Given that

is an algebraic identity, what is the value of a-b?

'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'

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,919

Hi Agnishom

I'd say it's

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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What on earth does the question mean?

'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'

'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: 94,541

For what values of a and b is that expression always true.

**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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How do you do that? (by hand)

'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'

'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: 94,541

First I would compute it to give me some insight.

After that, I would substitute x = 0 and x = 1 into that identity and solve for a and b simultaneously.

**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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Where do you get 0 and 1 from? Or are they just arbitary?

'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: 94,541

It is standard when you want to eliminate a parameter that does not count to just plug in any numbers. At the AOPS they go ape at this concept of guessing. We say, they know nothing. It is a little bit of an Ansatz!

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Equate the coefficients of x:

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"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,541

Hi gAr;

Yes, that is another way.

Hi Agnishom;

You do it with your package like this:

```
Solve[{a*x + 25 - 5 (x - b) == 0 /. x -> 1,
a*x + 25 - 5 (x - b) == 0 /. x -> 0}, {a, b}]
```

**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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no attacking other people please. What is the AOPS way?

'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: 94,541

It is a long story and perhaps sometime in the future we will talk about it. For the now, do you understand how to do this?

**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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Yes, thank you all.

If you would tell me the AOPS method, I'd learn another one.

'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: 94,541

Sorry, I did not learn any of their methods. Reppie mathematics makes me nauseous.

If you want a recommendation you should learn all of them but gAr's you should learn first.

**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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OK thank you. What is their method, anyway?

'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: 94,541

They never did show me any of their mighty methods, they just kept on saying how mine were bad. This always confused me, X has no answer to a question but says and thinks Y's method which got the right answer is stupid?! Reppie reasoning makes me nauseous.

You have 3 ways there, learn them.

**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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