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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

I have solved the following, but it seems impossible to factorise at some point:

3^2x+1 - 3^x+2 - 3^x+1 = 0.

The book says, x=-1 or -2

It was impossible for to factorise at some point, let alone getting the answer.

I need assistance.

Thanks.

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

please make the expression clear with brackets

eg 3^(2x+1) 0r 3^(2x) + 1

thanks

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

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

There is no bracket involved in it from where I copied.

It is treated under indices.

I have solved similar problem but this seems insoluble at some point.

I will solvd for you to see where I got stuck.

I know only one thing - that is that I know nothing

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

Here I go.

(3^x)^2 * 3 - 3^x*3^2 - 3^x*3 +1=0

Let 3^x = M. therefore substitution.

3m^2 - 9m - 3m + 1

= 3m^2 - 12m + 1=0

factorization seem impossible here.

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

I just wanted to be clear that the problem is:

If so then x = -1 and -2 are not solutions:

This is not zero.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

That can not be factored. You need as Bob suggests to clean the question up.

**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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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

I have solved a similar question successfuly, see.

3^2x+3 - 4(3^x+1) + 1=0

*Last edited by EbenezerSon (2013-07-22 07:30:52)*

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

Please bracket that a little better.

**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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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

That is how it exist in the book I am working with.

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

What does 3^2x+3 mean?

**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: 6,395

I think it is unlikely that a book would use the symbol ^

please look again at post 5

Is the equation I have put there the one in your book?

Bob

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

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

bobbym wrote:

What does 3^2x+3 mean?

It means the 3 has raised to the power 2x+3.

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hasn't he raised a good point with

bob bundy wrote:

I think it is unlikely that a book would use the symbol ^

I would agree, but you say it is there! But then his post #5 is correct and that is not a solution.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

bobbym wrote:

Hasn't he raised a good point with

bob bundy wrote:I think it is unlikely that a book would use the symbol ^

I would agree, but you say it is there! But then his post #5 is correct and that is not a solution.

The book did not use the symbol ^, I rather used it , because the 2x +3 is at the top of the 3 in the book.

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

This is exactly what is in the book then?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

bob bundy wrote:

I just wanted to be clear that the problem is:

If so then x = -1 and -2 are not solutions:

This is not zero.

Bob

Yes that's how it is arranged, in the book.

*Last edited by EbenezerSon (2013-07-22 07:03:09)*

I know only one thing - that is that I know nothing

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

bobbym wrote:

Hi;

This is exactly what is in the book then?

Yes Sir!. Positive 1 is at the end

*Last edited by EbenezerSon (2013-07-22 07:03:46)*

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

It is obviously some sort of typo.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

bobbym wrote:

It is obviously some sort of typo.

The book is before me now and has positive 1 just at the end.

*Last edited by EbenezerSon (2013-07-22 08:25:55)*

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

It still looks like a mistake in the book. -1 and -2 are not roots of that equation.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

Then please how exactly would the final answer be?

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

I could not solve that by hand. It takes a computer to solve it. The answer involves complex numbers further showing that the problem is mistyped.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 465

Yeb I must believe you, c'os the author stated explicitly that, a student should forgive any mistake that would be found in the book. Is just at the beginning of the book .

:-) But still you're darling!

*Last edited by EbenezerSon (2013-07-22 08:53:35)*

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

If you are marked wrong about it then you will have the consolation of knowing that I would have been marked wrong too.

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: 6,395

So now the question has become:

It still will not lead to those answers:

x = -1

x = -2

Closest equation with those answers that I can find:

Bob

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