Math Is Fun Forum

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

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.

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Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Algebra: Polynomial Question

hi math9maniac

I'm not seeing any real solutions.

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

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Algebra: Polynomial Question

Hi math9maniac,

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

Re: Algebra: Polynomial Question

Hi,

I agree with bob bundy's views.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

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.

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Only a friend tells you your face is dirty.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

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.

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Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

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.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

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

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Only a friend tells you your face is dirty.