- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,952

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

- Thread starter anemone
- Start date

- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,952

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

Am I correct in expecting that you wanted nonreal solutions?

- Thread starter
- Admin
- #3

- Feb 14, 2012

- 3,952

Yes,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?

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

- Mar 31, 2013

- 1,356

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

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)

- Thread starter
- Admin
- #6

- Feb 14, 2012

- 3,952

Bravo,(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)

- Mar 31, 2013

- 1,356

I would. Could you tell me how. As a matter of fact I do not knowBravo,kaliprasad! 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?

- Thread starter
- Admin
- #8

- Feb 14, 2012

- 3,952

HelloI would. Could you tell me how. As a matter of fact I do not know

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

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

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

- Mar 31, 2013

- 1,356

Hellokaliprasad,

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 thebutton 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

- Aug 30, 2012

- 1,308

Oh! And I thought the Sp button was a spell check!

Seriously I didn't know that. Thanks.

-Dan

Seriously I didn't know that. Thanks.

-Dan

- Admin
- #11

- Mar 5, 2012

- 9,773

Well, since it was not specified anywhere, the roots might also be for instance quaternions.Well, no it didn't, neither in the title nor the main body, but no matter. I'll get back to you

(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.

- Admin
- #12