Is a rational number? Prove your answer.

I know it isn't and that I need to rewrite in the form , but I'm having trouble doing so.

Printable View

- Dec 3rd 2009, 03:00 PMPinkkIs the following a rational number?
Is a rational number? Prove your answer.

I know it isn't and that I need to rewrite in the form , but I'm having trouble doing so. - Dec 3rd 2009, 05:09 PMDrexel28
- Dec 3rd 2009, 05:40 PMDrexel28
P.S. - Wolfram|Alpha

- Dec 3rd 2009, 06:04 PMPinkk
- Dec 3rd 2009, 06:06 PMDrexel28
- Dec 3rd 2009, 06:28 PMPinkk
Hmm, well, assuming that , then

, which is a contradiction since the product of a rational and an irrational cannot be rational. - Dec 4th 2009, 08:56 PMPinkk
Argh, I made a careless mistake, so what I posted above is clearly wrong. I am stuck on how to show the sum of those two irrationals must be irrational. (Headbang)(Headbang)(Headbang)

- Dec 4th 2009, 09:07 PMSampras
- Dec 4th 2009, 09:10 PMPinkk
Well yes, which is exactly why I don't know how to make the conclusion that is irrational.

- Dec 4th 2009, 09:17 PMDrexel28
- Dec 5th 2009, 07:03 AMPinkk
Bleh, I can't see how that helps. (Headbang)

Any suggestions please? I'm sorry for the excessive posting but I really need to know how to show a formal proof for this. - Dec 6th 2009, 01:13 PMevry1cndie
Hey Pinkk, I've gone as far as expanding the polynomial to x^72, but still have some ways to go in order to use the rational roots theorem. I'm just as clueless as to how the hell to work this out any other way, seeing as we can't assume that the sum of two irrationals is going to be irrational. I think there was some sort of underestimation as to how difficult this problem really is using the knowlege we have. I think it's just a combination of a few problems from the yellow book and was figured that it couldn't be too much harder than the others... i dunno, let me know if you make any progress, i've just about given up.

- Dec 6th 2009, 01:38 PMPinkk
Nope, I've given up on it, it's just way too tedious and there's no guarantee that approach will work.

Edit: A professor at our college provided hints/solutions for these problems:

http://mathbin.net/38158

http://mathbin.net/38159

http://mathbin.net/38160