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Roots Finding Challenge

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anemone

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Feb 14, 2012
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Find the four roots of the equation $(x-3)^4+(x-5)^4+8=0$.
 

Prove It

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Jan 26, 2012
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Find the four roots of the equation $(x-3)^4+(x-5)^4+8=0$.
There aren't any real roots, each of the fourth powers is nonnegative, and so adding 8 means that it can never equal 0.

Am I correct in expecting that you wanted nonreal solutions? :p
 
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anemone

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Feb 14, 2012
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There aren't any real roots, each of the fourth powers is nonnegative, and so adding 8 means that it can never equal 0.

Am I correct in expecting that you wanted nonreal solutions? :p
Yes, Prove It! The question asked for the 4 non-real roots and now, I'm expecting you to solve it!(Tongueout)
 

Prove It

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Yes, Prove It! The question asked for the 4 non-real roots and now, I'm expecting you to solve it!(Tongueout)
Well, no it didn't, neither in the title nor the main body, but no matter. I'll get back to you :)
 

kaliprasad

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Mar 31, 2013
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Well, no it didn't, neither in the title nor the main body, but no matter. I'll get back to you :)
(x−3)^4+(x−5)^4+8=0.

put x - 4 = y to get

(y+1)^4 + (y-1) ^4 + 8 = 0

or 2(y^4+ 6y^2+1) + 8 = 0

or y^4 + 6y^2 + 5 = 0

(y^2 + 1)(y^2 + 5) = 0

y = i, - i, i sqrt(5), - i sqrt(5)

or x = 4+i, 4- i, 4+ i sqrt(5),4 - i sqrt(5)
 
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anemone

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Feb 14, 2012
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(x−3)^4+(x−5)^4+8=0.

put x - 4 = y to get

(y+1)^4 + (y-1) ^4 + 8 = 0

or 2(y^4+ 6y^2+1) + 8 = 0

or y^4 + 6y^2 + 5 = 0

(y^2 + 1)(y^2 + 5) = 0

y = i, - i, i sqrt(5), - i sqrt(5)

or x = 4+i, 4- i, 4+ i sqrt(5),4 - i sqrt(5)
Bravo, kaliprasad! (Clapping)And thanks for participating too...though I'd appreciate it if you would hide your solution whenever you decided to answer to any of the challenge problems...if you're okay with that, do you know how to hide your solution?
 

kaliprasad

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Mar 31, 2013
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Bravo, kaliprasad! (Clapping)And thanks for participating too...though I'd appreciate it if you would hide your solution whenever you decided to answer to any of the challenge problems...if you're okay with that, do you know how to hide your solution?
I would. Could you tell me how. As a matter of fact I do not know
 
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anemone

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Feb 14, 2012
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I would. Could you tell me how. As a matter of fact I do not know
Hello kaliprasad,

The easiest way I know of to accomplish this is to compose your reply as normal, and then when you are finished, but before submitting the post, select the portion of your post that contains the actual solution using your mouse or keyboard. Then while this text is selected, click the
button on the far right of the middle row of the toolbar, and this will generate the spoiler tags to enclose the selected text. Then preview your post to make sure it looks like you intend.

Here is an image of the button to click to enclose the selected text with the spoiler tags:
belleforkali.png

Feel free to ask if you have any problems getting this to work.
 

kaliprasad

Well-known member
Mar 31, 2013
1,309
Hello kaliprasad,

The easiest way I know of to accomplish this is to compose your reply as normal, and then when you are finished, but before submitting the post, select the portion of your post that contains the actual solution using your mouse or keyboard. Then while this text is selected, click the
button on the far right of the middle row of the toolbar, and this will generate the spoiler tags to enclose the selected text. Then preview your post to make sure it looks like you intend.

Here is an image of the button to click to enclose the selected text with the spoiler tags:
View attachment 1353

Feel free to ask if you have any problems getting this to work.


Thanks

I got it if this part is enclosed else I did not
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
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Oh! And I thought the Sp button was a spell check! ;)

Seriously I didn't know that. Thanks.

-Dan
 

Klaas van Aarsen

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Mar 5, 2012
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Well, no it didn't, neither in the title nor the main body, but no matter. I'll get back to you :)
Well, since it was not specified anywhere, the roots might also be for instance quaternions.
(I just liked saying that.)
Luckily it suffices that they are complex. ;)
To be honest, I was also confused for a moment when I realized there were no real solutions.
 

MarkFL

Administrator
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Feb 24, 2012
13,775
I took the question to mean "find the 4 roots" regardless of their nature. :D