From the Mayhem. (Again)

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Ashfaq Uday
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From the Mayhem. (Again)

Unread post by Ashfaq Uday » Thu Nov 03, 2011 7:43 pm

Let\[\left \lfloor x \right \rfloor\]be the greatest integer not exceeding\[x\]
and let\[\left \{ x \right \}\]be the fractional part of the real number\[x\].
Find all positive real number\[x\]
such that\[\left \{ \left (2x+3 \right )/\left (x+2 \right ) \right \} + \left \lfloor \left ( 2x+1 \right )/\left ( x+1 \right ) \right \rfloor = 14/9\]


I'm just getting started with latex (I know um aweful! at it) and BDMO. expect more contribution from me. :D

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nafistiham
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Re: From the Mayhem. (Again)

Unread post by nafistiham » Fri Nov 04, 2011 6:20 pm

i am not sure whether it is right or not, but my solution is such
\[\left \{\frac{2x+3}{x+2}\right \}+\left \lfloor \frac{2x+1}{x+1} \right \rfloor=\frac{14}{9}\]
\[\Rightarrow \left \{ 1+\frac{x+1}{x+2}\right \} +\left \lfloor 1+\frac{x}{x+1} \right \rfloor= \frac{14}{9}\]
\[\Rightarrow \frac{x+1}{x+2}+1= \frac{14}{9}\]
\[\Rightarrow 18x+27=14x+28\]
\[\Rightarrow 4x=1\]
\[\Rightarrow x= \frac {1} {4}\]
here is just a little experience about $LaTeX$ which may help you.

just have an one hour experiment with the equation editor :D :D


and, to the authority - i think this topic should be moved to any other problem forum,as it is not any part of BDMC
Last edited by nafistiham on Fri Nov 04, 2011 10:49 pm, edited 1 time in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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*Mahi*
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Re: From the Mayhem. (Again)

Unread post by *Mahi* » Fri Nov 04, 2011 10:07 pm

nafistiham wrote:i am not sure whether it is right or not, but my solution is such
\[{\frac{2x+3}{x+2}}+\left \lfloor \frac{2x+1}{x+1} \right \rfloor=\frac{14}{9}\]

and, to the authority - i think this topic should be moved to any other problem forum,as it is not any part of BDMC
Seems like you missed a $\{ \}$ there... must be a typing mistake...
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

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nafistiham
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Re: From the Mayhem. (Again)

Unread post by nafistiham » Fri Nov 04, 2011 10:47 pm

:oops: :oops: :oops:

sorry. editing that. but is the solution all ok?
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

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*Mahi*
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Re: From the Mayhem. (Again)

Unread post by *Mahi* » Fri Nov 04, 2011 10:58 pm

I think so too.
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

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