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#326 2014-08-27 07:03:42

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

Polynomials are in the book,  but I am yet to learn them properly.


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#327 2014-08-27 07:10:36

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

By the way, if you can supply me with a link that teaches or deals with polynomial happy will I be
Besides, those problems are treated under indices

Thanks

Last edited by EbenezerSon (2014-08-27 07:13:11)


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#328 2014-08-27 07:15:07

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

Re: Simplify the following:

Hi;

I am unable to solve either of those equation separately without using factoring or the quadratic formula. I will leave the question here and maybe someone else can do it. I am drawing a blank, sorry.


Can anyone solve these equations?

1)

2)


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.

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#329 2014-08-27 07:21:34

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

At the back of the book it gave these as it answers; {x : x = -1, -2}

I will try to solve, I doubt if will get those answers.

Thank you Bobbym

Last edited by EbenezerSon (2014-08-27 07:24:52)


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#330 2014-08-27 08:00:35

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

Re: Simplify the following:

Yes, those are the correct answers. Sorry, I could not do them.


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.

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#331 2014-08-27 09:30:36

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

Hi;
I have endeavored to solve them, I literally used hours,  which I had {-1, -2} for the first one and {-1} for the second problem. At the back of the book it has {-1} as the answer for the second problem,  so I think I am correct.
Did you say you used factorization and quadratic to solve them, and what are your answers?
Thanks


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

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#332 2014-08-27 23:45:11

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

Re: Simplify the following:

Those are the correct answers by factorization. How did you do the first one without it?


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.

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#333 2014-08-28 03:59:03

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

Actually with respect to the first one I did used factorization in the course of manipulation, see;

4 3^(2x+1) + 17 3^X -7 = 0
= 4 (3^x)^2 3^1  + 17 (3^x) - 7 = 0
Let 3^x = M
= 4 M^2 3 + 17M - 7 = 0
= 12M^2 - 4M + 21M - 7= 0
= 4M(3M - 1) + 7(3M - 1) = 0
=(4M + 7) (3M - 1) = 0
   Let M = 3^x.
4M + 7 = 0
= 4M = -7
=M = -7/4
Again,
3M - 1 = 0
3M = 1
M = 1/3 Let 3^x = M
3^x = 1/3
3^x= 3^-1.
x = -1

I used the same method to do the first one

Last edited by EbenezerSon (2014-08-28 04:01:08)


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

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#334 2014-08-28 04:05:07

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

Re: Simplify the following:

That is what I did! I am sorry, I thought you would not understand it so I did not post it.


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.

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#335 2014-08-28 04:25:32

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

The first one;
proceeding from the question:

3^2x 3^3 - 4 (3^x 3) + 1 = 0
= 3^2x 27 - 4(3^x 3) + 1 = 0
= (3^x)^2 27 - 4(M 3) + 1 = 0
  Let 3^x = M
(3^x)^2 27 - 4 (M 3) + 1 = 0
= 27M^2 - 12M + 1 = 0
= 27M^2 - 9M - 3M + 1 = 0
= 9M(3M - 1) - 1(3M - 1)= 0
= (9M - 1) (3M - 1) = 0
Let M = 3^X
9M - 1 = 0
M = 1/9
3^X = 1/9 = 3^ -2 = -2
X = -2

3M - 1 = 0
M = 1/3
3^X = 1/3 = 3^-1 = -1

{ X : X = -1, -2}


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#336 2014-08-28 04:31:11

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

Re: Simplify the following:

That is very good.


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.

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#337 2014-08-28 04:34:10

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

Hi Bobbym please help with this;

Find the value of x in the following equation

2^x - 2^-x = 2
This is similar to the one we solved previously,  I tried and had [0] as an answer yet don't understand


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#338 2014-08-28 04:41:04

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

Re: Simplify the following:

Multiply both sides by 2^x and do what you did before.


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.

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#339 2014-08-28 05:03:07

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

Following the question;

= 2^2x - 1 = 2^(1+x)
= (2^x)^2 - 2^(1+x) = 0
  Let 2^x = N
= N^2 - 2N - 1 = 0
Factorizing impossible!
What do you say?
If factorization is impossible should one use log? Or the method of completing the square?


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

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#340 2014-08-28 05:15:33

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

Re: Simplify the following:

That can not be factored, you are correct. We need another way.


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.

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#341 2014-08-28 05:28:48

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

The book has at it back zero [0] as its answer, please do it for me to see by using log, I am certain you can get by log application
Thanks!


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

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#342 2014-08-28 05:31:35

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

Re: Simplify the following:

Have you copied the problem correctly?

2^x - 2^-x = 2 does not have zero for a root.


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.

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#343 2014-08-28 05:36:52

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

Yes that is exactly what's in the book, I have double check it.


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#344 2014-08-28 05:37:55

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

Re: Simplify the following:

Please plug in x = 0 and tell me what you get?


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.

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#345 2014-08-28 05:42:10

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

2^0 -  2^ 0 =
1 - 1 = 0 I got zero


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#346 2014-08-28 05:44:24

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

Re: Simplify the following:

Does 0 equal 2?


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.

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#347 2014-08-28 05:47:49

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

The book is wrong, I will be inclined to say that, what do you think should be the method that will eventually give you the correct answer?


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

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#348 2014-08-28 05:49:45

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

Re: Simplify the following:

I think the same method to factor but use the quadratic formula to get the roots will get the answer.

I also think the book meant to solve this problem instead.

2^x + 2^-x = 2


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.

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#349 2014-08-28 05:55:19

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Simplify the following:

bobbym wrote:

I think the same method to factor but use the quadratic formula to get the roots will get the answer.
(I don't get you here)

I also think the book meant to solve this problem instead.
I am very sure!

2^x + 2^-x = 2


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

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#350 2014-08-28 06:00:56

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

Re: Simplify the following:

You will get the polynomial when you use the substitution of y = 2^x of y^2 - 2y - 1 = 0.


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.

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