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#1 2012-12-17 23:55:37

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,646
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Can you find x^5 + 1/(x^5) without solving for x?

If x^2 - 3x + 1 = 0
then find x^5 + 1/x^5


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2012-12-18 00:11:57

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

Hi Agnishom;


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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#3 2012-12-18 00:26:32

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,646
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Re: Can you find x^5 + 1/(x^5) without solving for x?

What do I need to know in order to find out the expansion of (x +1/x)^5?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2012-12-18 00:31:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

All problems have a trick associated with them. Good problem solvers have lots of tricks up their sleeves.

All these problems are solved by turning something of the form

Notice how artificially the polynomial given expands into that form.


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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#5 2012-12-18 00:35:21

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,646
Website

Re: Can you find x^5 + 1/(x^5) without solving for x?

bobbym wrote:


]

How do I get this? Do I need the binomial theorem?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2012-12-18 00:37:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

Exactly or Pascals triangle.


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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#7 2012-12-18 00:41:07

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,646
Website

Re: Can you find x^5 + 1/(x^5) without solving for x?

Hmm... Thanks!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#8 2012-12-18 00:45:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

Hi Agnishom;

You are welcome. Please have patience you are improving. "All things come to he who waits - pappym.


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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#9 2012-12-18 01:08:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,646
Website

Re: Can you find x^5 + 1/(x^5) without solving for x?

Pappym? Your dad?
If you don't mind, is "bobbym" your real name?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#10 2012-12-18 01:13:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

Yes, pappym was my dear old Dad. A good ole boy from deep in Alabama.

[removed]


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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#11 2012-12-18 06:55:42

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

Re: Can you find x^5 + 1/(x^5) without solving for x?

And what was removed?

I really like the "Pass me the chicken" quote from pappym.


“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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#12 2012-12-18 07:07:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

anonimnystefy wrote:

And what was removed?

My real age of course!


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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#13 2012-12-18 08:51:31

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

Re: Can you find x^5 + 1/(x^5) without solving for x?

Who asked you about your age? Agnishom asked you about your name...


“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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#14 2012-12-18 08:58:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

That he did. That was removed also.


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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#15 2012-12-18 16:49:02

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,646
Website

Re: Can you find x^5 + 1/(x^5) without solving for x?

So, bobbym wants to be more anonymous than anonymnistefy?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#16 2012-12-18 19:11:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,309

Re: Can you find x^5 + 1/(x^5) without solving for x?

If I wanted to be anonymous I would not have told you the answers.


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.

Offline

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