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#1 2018-09-30 23:30:49

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 414

Algebra: Polynomial Question

Hello friends,

It has been a while. Other things than math have taken my time. I trust you're well. Please help me with this question. I couldn't help my friend and she needs the answer in few hours

√x  -  x^4 = √2. Find x.

Many thanks in advance.


Only a friend tells you your face is dirty.

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#2 2018-10-01 01:04:44

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,417

Re: Algebra: Polynomial Question

hi math9maniac

I'm not seeing any real solutions.

https://www.mathsisfun.com/data/functio … t(x) - x^4

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

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#3 2018-10-01 01:12:02

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,213
Website

Re: Algebra: Polynomial Question

Hi math9maniac,

Can I just check that the equation you wrote down is correct?

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#4 2018-10-01 01:13:52

ganesh
Administrator
Registered: 2005-06-28
Posts: 26,432

Re: Algebra: Polynomial Question

Hi,

I agree with bob bundy's views.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#5 2018-10-01 03:58:36

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 414

Re: Algebra: Polynomial Question

I'm baffled because I don't know how it is possible to evaluate the LHS; never seen anything of this kind.


Only a friend tells you your face is dirty.

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#6 2018-10-01 04:02:35

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 414

Re: Algebra: Polynomial Question

Hi zetafunc,

Your question made me just ask my friend again. She says she composed that from the question. The original question, she says, is actually:

√(x - b) = x^4. Find x, if b = 2.

Please help me again family.


Only a friend tells you your face is dirty.

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#7 2018-10-01 19:34:49

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,417

Re: Algebra: Polynomial Question

hi math9maniac

The 'simplification' was not valid.  √ (A-B) is not generally equal to √ A - √ B

I squared both sides of the equation to get

I'm still not seeing any real solutions.  See https://www.mathsisfun.com/data/functio … ^8 - x + 2

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

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#8 2018-10-02 15:43:53

Grantingriver
Member
Registered: 2016-02-01
Posts: 105

Re: Algebra: Polynomial Question

The bob bundy argument is in fact correct (as usual), this equation has no solution in the real field. However, since you did not specify the field of the required solution this opens the door to consider a solution in other fields. Form this respect, it has a solution in the complex field and in the field of residue classes modulo 7. In the complex field it has eight roots namely:


and there is a unique solution in the field of residue classes modulo 7 which is a finite field consisting of the following elements:

so by noticing that:

the unique solution, in this field, will be:

In fact it can be shown that there are, in principle, many fields that can be created which have solutions to this equation, the above solutions are just tow instances of them.

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#9 2018-10-05 02:33:59

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 414

Re: Algebra: Polynomial Question

Hello,

Thank you all so much for taking the time to help out. I do appreciate. It appears there is no solution for the question. There must have been an error in whatever book from which my mate sent me that question.

Regards,
math9maniac


Only a friend tells you your face is dirty.

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