Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

please make the expression clear with brackets

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

thanks

Children are not defined by school ...........The Fonz

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

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

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

Children are not defined by school ...........The Fonz

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Please bracket that a little better.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

What does 3^2x+3 mean?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

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

Children are not defined by school ...........The Fonz

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

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

This is exactly what is in the book then?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

It is obviously some sort of typo.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

Then please how exactly would the final answer be?

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 551

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

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

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

Offline