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Home » Mathematics » Middle School Contests (MATHCOUNTS, AMC 8, MOEMS, Ages 10-13)
 
Mathcounts Challenge: Reciprocol of X!
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Syntax Error
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#1
Mathcounts Challenge: Reciprocol of X!
suppose a number x satisfies x^2-4x-1=0. How much greater is x than its reciprocals!


lolt, i put an exclamation point instead of an "?". wooooot
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PostPosted: Sun Sep 07, 2003 3:22 pm  Back to top 
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#2
*sigh* sorry to reprimand you, but I don't think "wooooot" is appropriate, but it is funny Smile oh well.

and I know, I know. I should go worry about somat else, right? Smile

PostPosted: Sun Sep 07, 2003 3:24 pm  Back to top 
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#3
in a word...yes
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PostPosted: Sun Sep 07, 2003 3:26 pm  Back to top 
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#4
Is there four answers to this?

PostPosted: Sun Sep 07, 2003 3:43 pm  Back to top 
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MysticTerminator
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#5
no.

hint if you want it Click to reveal hidden content
note that the amount asked for in the problem is x-1/x. Hmmmm that looks familiar...I wonder what would happen if we multiplied it by something...

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#6
Oh yeah.

PostPosted: Sun Sep 07, 2003 3:54 pm  Back to top 
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#7
all you need is a bit of manipulation
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PostPosted: Sun Sep 07, 2003 3:59 pm  Back to top 
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Fierytycoon
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#8
Yes...I too am wondering...

Question
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PostPosted: Sun Sep 07, 2003 4:00 pm  Back to top 
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#9
Re: Mathcounts Challenge: Reciprocol of X!
Syntax Error wrote:
suppose a number x satisfies x^2-4x-1=0. How much greater is x than its reciprocals!



Spoiler:Click to reveal hidden content

so divide x^2-4x-1=0 by x to get x-4-1/x=0, or x-1/x=4
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PostPosted: Sun Sep 07, 2003 4:01 pm  Back to top 
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Fierytycoon
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#10
..So the answer is true for any x, not just for the roots, right?
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PostPosted: Sun Sep 07, 2003 4:03 pm  Back to top 
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MysticTerminator
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#11
correct, but to be absolutely certain Click to reveal hidden content
x cannot be 0, because it does not satisfy the equation, which is why we can divide through by x


Wink

fierytycoon, no, it's just for the roots.
Last edited by MysticTerminator on Sun Sep 07, 2003 4:05 pm; edited 1 time in total 
PostPosted: Sun Sep 07, 2003 4:04 pm  Back to top 
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#12
I guess. but it's still kind of feels weird...and I feel weird saying this because I should know this stuff as the comoderator, but don't. Smile

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#13
its okay, to clear up the 0 thing further, 1/0 is undefined, because if 1/0=0, multiplying both sides by 0, 1=0. and thats not true. i think mystic may have said that also, but i just skimmed it
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PostPosted: Sun Sep 07, 2003 4:10 pm  Back to top 
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#14
Actually, I said that, but oh well. I'll go worry about other things now Smile (Like the fact that I didn't solve the question Sad )

PostPosted: Sun Sep 07, 2003 4:11 pm  Back to top 
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TheSouthpaw
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#15
Click to reveal hidden content


4

PostPosted: Sun Sep 07, 2003 4:23 pm  Back to top 
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#16
It gets really annoying when you post solutions without the thinking process, especially when someone else already answered the question.

Am I sounding too harsh? :twisted:

PostPosted: Sun Sep 07, 2003 4:25 pm  Back to top 
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Fierytycoon
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#17
No, but with Neal's solution, you could do that with any x, not just for the roots.
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#18
I wasn't talking about neal...

PostPosted: Sun Sep 07, 2003 4:26 pm  Back to top 
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Fierytycoon
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#19
I wasn't talking about you...
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PostPosted: Sun Sep 07, 2003 4:27 pm  Back to top 
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#20
Question Shocked *drool*
I'm Confused ...

PostPosted: Sun Sep 07, 2003 4:31 pm  Back to top 
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