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

You are not logged in.

#1 2013-07-22 03:02:49

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Find the truth set of the following.

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

#2 2013-07-22 03:09:20

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: Find the truth set of the following.

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

Offline

#3 2013-07-22 03:39:13

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#4 2013-07-22 04:02:28

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#5 2013-07-22 04:15:17

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: Find the truth set of the following.

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

Offline

#6 2013-07-22 04:17:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#7 2013-07-22 04:54:57

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#8 2013-07-22 05:00:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

Hi;

Please bracket that a little better.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9 2013-07-22 05:21:06

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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


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

Offline

#10 2013-07-22 05:22:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

What does 3^2x+3 mean?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#11 2013-07-22 05:31:15

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: Find the truth set of the following.

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

Offline

#12 2013-07-22 06:37:09

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#13 2013-07-22 06:44:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#14 2013-07-22 06:51:24

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#15 2013-07-22 06:58:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

Hi;

This is exactly what is in the book then?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#16 2013-07-22 07:00:19

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#17 2013-07-22 07:01:28

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#18 2013-07-22 07:04:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

It is obviously some sort of typo.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#19 2013-07-22 07:09:34

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#20 2013-07-22 07:35:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#21 2013-07-22 07:45:58

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

Then please how exactly would the final answer be?


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

Offline

#22 2013-07-22 07:53:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#23 2013-07-22 08:53:08

EbenezerSon
Member
Registered: 2013-07-04
Posts: 466

Re: Find the truth set of the following.

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

#24 2013-07-22 08:55:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: Find the truth set of the following.

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#25 2013-07-22 09:50:40

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: Find the truth set of the following.

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

Board footer

Powered by FluxBB