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Topic: One Real Solution (Read 756 times) |
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gruff
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One Real Solution
« on: May 12th, 2007, 7:58am » |
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No-one seems to have posted on this puzzle yet. I think there are two real solutions to the simultaneous equations. One equation is a polynomial of order 17 and the other 16 which means subtracting them will give a positive and a negative root.
Has anyone else looked at it?
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Icarus
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Re: One Real Solution
« Reply #1 on: May 12th, 2007, 11:20am » |
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To get polynomials, you have to multiply each equation through by x. Once you subtract the two equations, you get a polynomial of degree 18.
(x+1)18 - (x+1)17 - x
The real roots of even degree polynomials come in pairs, though sometimes the pairs consist of the same root given twice. In that case, though, the root will also be a root of the derivative. But
18(18/17)17 - 17(18/17)16 - 1 > 4,
so x = 1/17 is not a multiple root.
So there has to be a second root somewhere, doesn't there.
Or does there? 
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| « Last Edit: May 12th, 2007, 11:31am by Icarus » |
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ThudnBlunder
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Re: One Real Solution
« Reply #2 on: May 12th, 2007, 2:15pm » |
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on May 12th, 2007, 7:58am, gruff wrote:No-one seems to have posted on this puzzle yet.
Has anyone else looked at it? |
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Yes, in fact there is already a thread about it.
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Eigenray
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Re: One Real Solution
« Reply #3 on: May 12th, 2007, 2:21pm » |
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Yes, the number of solutions to the simultaneous equations is certainly even.
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gruff
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Re: One Real Solution
« Reply #4 on: May 13th, 2007, 3:45am » |
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on May 12th, 2007, 2:15pm, ThudanBlunder wrote:
Yes, in fact there is already a thread about it. |
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Where? I looked for ages.
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ThudnBlunder
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Re: One Real Solution
« Reply #5 on: May 13th, 2007, 4:09am » |
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on May 13th, 2007, 3:45am, gruff wrote:
Where? I looked for ages. |
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Rather than 'look for' you should use the search function.
Voilį.
(By the way, welcome to the forum.) 
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| « Last Edit: May 13th, 2007, 4:24am by ThudnBlunder » |
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gruff
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Re: One Real Solution
« Reply #6 on: May 13th, 2007, 6:47am » |
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on May 13th, 2007, 4:09am, ThudanBlunder wrote:
Rather than 'look for' you should use the search function.
Voilį.
(By the way, welcome to the forum.)
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I not only looked for quite a while, I searched for quite a while too. I searched for every combination of the words "one real solution" plus the numbers 18 and 17 since these are in the problem. I found nothing of relevance to the puzzle. If threads aren't named by the name of the problem and don't contain relevant terms they don't appear in the search results.
Since you seem to have found it, it would be helpful if you could post a link.
Thanks.
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rmsgrey
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Re: One Real Solution
« Reply #7 on: May 13th, 2007, 6:56am » |
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on May 13th, 2007, 6:47am, gruff wrote:
Since you seem to have found it, it would be helpful if you could post a link.
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He did - the word "Voilį"...
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BNC
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Re: One Real Solution
« Reply #8 on: May 13th, 2007, 6:59am » |
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on May 13th, 2007, 6:47am, gruff wrote:
I not only looked for quite a while, I searched for quite a while too. I searched for every combination of the words "one real solution" plus the numbers 18 and 17 since these are in the problem. I found nothing of relevance to the puzzle. If threads aren't named by the name of the problem and don't contain relevant terms they don't appear in the search results.
Since you seem to have found it, it would be helpful if you could post a link.
Thanks.
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The default "latest post" field is one year. You should change it manually to search for older threads (like this one). Try searching "one real solution", using "as a whole phrase" and change the time setting, say, 10 years.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Icarus
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Re: One Real Solution
« Reply #9 on: May 13th, 2007, 12:27pm » |
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Actually, google is an easier method for searching for threads than the built-in search function. Just set it up as a site search of www.ocf.berkeley.edu and include "wu" and "forums" as keywords.
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| « Last Edit: May 14th, 2007, 3:50pm by Icarus » |
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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gruff
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Re: One Real Solution
« Reply #10 on: May 14th, 2007, 3:42am » |
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on May 13th, 2007, 6:56am, rmsgrey wrote:
He did - the word "Voilį"... |
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Doh!
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