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        riddles >> putnam exam (pure math) >> Simplify Expression
        
(Message started by: ThudanBlunder on Aug 27th, 2007, 2:44pm)
Title: Simplify Expression
Post by ThudanBlunder on Aug 27th, 2007, 2:44pm
Simplify

[(11 + 5http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif5)/2]1/5 + [(76 - 34http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif5)/2]1/9
Title: Re: Simplify Expression
Post by towr on Aug 27th, 2007, 2:58pm
hmmm.. Whatever could [hide][phi5]1/5 + [(1-phi)9]1/9[/hide] be  ;)
Title: Re: Simplify Expression
Post by mikedagr8 on Aug 27th, 2007, 6:07pm
Hooray, it looks like I can do this question, but I have logs to do. [hide]It is 3.116044297 according to my calculator  :P[/hide]
Title: Re: Simplify Expression
Post by ThudanBlunder on Aug 27th, 2007, 6:30pm

on 08/27/07 at 18:07:40, mikedagr8 wrote:
Hooray, it looks like I can do this question, but I have logs to do. [hide]It is 3. according to my calculator  :P[/hide]

GIGO

Title: Re: Simplify Expression
Post by Sameer on Aug 27th, 2007, 7:03pm
It is [hide] lne [/hide] ;)
Title: Re: Simplify Expression
Post by denis on Aug 27th, 2007, 8:15pm
[hide]0.999......[/hide] ;)
Title: Re: Simplify Expression
Post by Barukh on Aug 27th, 2007, 11:28pm

on 08/27/07 at 14:58:54, towr wrote:
hmmm.. Whatever could [hide][phi5]1/5 + [(1-phi)9]1/9[/hide] be  ;)

Wow! [hide]Is it irrational[/hide]?
Title: Re: Simplify Expression
Post by mikedagr8 on Aug 28th, 2007, 2:22am
GIGO?
What does this mean, also what about ROLOL?
Lost about this.
Title: Re: Simplify Expression
Post by ThudanBlunder on Aug 28th, 2007, 2:36am

on 08/28/07 at 02:22:09, mikedagr8 wrote:
GIGO?
What does this mean, also what about ROLOL?

GIGO = Garbage In, Garbage Out
ROLOL should be ROTFL
Title: Re: Simplify Expression
Post by mikedagr8 on Aug 28th, 2007, 2:49am
GIGO, thats the translation, but what does it actually mean, that I am incorrect? I'm not, I simplified it.
Title: Re: Simplify Expression
Post by towr on Aug 28th, 2007, 2:59am

on 08/28/07 at 02:49:43, mikedagr8 wrote:
GIGO, thats the translation, but what does it actually mean, that I am incorrect? I'm not, I simplified it.
You are incorrect. Your calculator may be ill-suited to simplify it.
You can simplify the first term easy enough (do you recognize the value?) But for the second term, you have to take the 9th root of a negative number. If your calculator is willing to do it at all, it might take the wrong one. (There are 9 options, but only one is correct in this context)

[e]My calculator seems to do it fine. I seem to recall having math programs/calculators screw up in similar problems though[/e]
Title: Re: Simplify Expression
Post by mikedagr8 on Aug 28th, 2007, 3:21am
1.618033989 sounds like the golden ratio to me...

I typed it incorrectly in the original response I think.

I'm going with denis on this one.
Title: Re: Simplify Expression
Post by towr on Aug 28th, 2007, 3:29am

on 08/28/07 at 03:21:59, mikedagr8 wrote:
1.618033989 sounds like the golden ratio to me...
Yes, the calculator doesn't do it justice with rounding it off of course. It is exactly (1+http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif5)/2
Once I had this, I guessed the other would be (1-http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif5)/2, because that's the kind of person I think Thud is ;)
(In any case I'd have expected the final answer to be an integer; because that's the kind of neat result you'd expect from a puzzle like this; and of course there were a few similar puzzles like this a while back)
Title: Re: Simplify Expression
Post by denis on Aug 28th, 2007, 5:31am

on 08/28/07 at 03:21:59, mikedagr8 wrote:
1.618033989 sounds like the golden ratio to me...

I typed it incorrectly in the original response I think.

I'm going with denis on this one.


Actually my answer wasn't derived by calculator. It was a veiled reference to another "puzzle" (the one where 0.9999...=1 where 9's are repeated ad infinitum)
Title: Re: Simplify Expression
Post by ThudanBlunder on Aug 28th, 2007, 5:47am

on 08/28/07 at 03:29:18, towr wrote:
because that's the kind of person I think Thud is ;)

Yes, naturally well-balanced and even-handed, that's me.   ;)

In general, [(L(n) + F(n)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif5)/2]1/n http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/pm.gif [(L(k) - F(k)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif5)/2]1/k = 1
If k is odd we take the plus sign.
If k is even we take the minus sign.
Title: Re: Simplify Expression
Post by mikedagr8 on Aug 28th, 2007, 3:34pm
ROTFLOL TB. Hahaha, nice


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