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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'

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Hi Agnishom

I'd say it's

.Here lies the reader who will never open this book. He is forever dead.

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

The knowledge of some things as a function of age is a delta function.

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,372

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

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,372

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

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,372

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

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

Equate the coefficients of x:

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"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: 106,372

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

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,372

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

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,372

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

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,372

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

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