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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

-2 is a solution to the equation

It arises because of the method of solution.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi bobbym

That is based on the simplicity of the solution. If it was something worse, you wouldn't be able to substitute and check easily without a computer.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

You are missing the point.

1) Why must it be easy to plug in? Does that invalidate the solution?

2) There are some obvious faults with the whole idea and I only presented it when I was sure the OP had already been satisfied.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

I never said it di have to be easy. i am just saying that there should be another way of checking that doesn't require plugging in, because the solution may not be always pretty and a computer might not always be the when you need it.

The solution has no flaws except that you didn't set any restrictions.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Does that invalidate the quadratic formula, or completing the square or any other way to get roots? You are always required to check the roots! Also with combinatoric problems too...

Kaboobly doo with the restrictions.

**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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

I agree. You should always check any answers you get.

Consider this:

A rectangle is 3 cm longer than it is wide. It has an area of 40 cm^2.

So, let the width be x => the length is x + 3 => the area is x(x + 3)

So answers may appear than are not solutions (unless you want to make a new topic in maths with 'negative lengths' )

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

The concept of negative length I think already exists, but not in regular geometry.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

There is also one more reason to check.

**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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