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Share/Save/Bookmark Login/ Register to Bookmark Topic : "sqaures" Started by Anirudh

Anirudh

#1 Posted 7:03pm 03-02-10  

sqaures

[im]http://codecogs.izyba.com/gif.latex?a_%7B1%7D%5E%7B2%7D+%20a_%7B2%7D%5E%7B2%7D+a_%7B3%7D%5E%7B2%7D%3D%2025[/im]

[im]http://codecogs.izyba.com/gif.latex?b_%7B1%7D%5E%7B2%7D+b_%7B2%7D%5E%7B2%7D+b_%7B3%7D%5E%7B2%7D%3D100[/im]

[im]http://codecogs.izyba.com/gif.latex?b_%7B1%7Da_%7B1%7D+b_%7B2%7Da_%7B2%7D+b_%7B3%7Da_%7B3%7D%3D%2050[/im]

[im]http://codecogs.izyba.com/gif.latex?Find%20%5C%3B%20%5C%3B%20%5Cfrac%7Ba_%7B1%7D%5E%7Bn%7D+a_%7B2%7D%5E%7Bn%7D+a_%7B3%7D%5E%7Bn%7D%7D%7Bb_%7B1%7D%5E%7Bn%7D+%20b_%7B2%7D%5E%7Bn%7D+b_%7B3%7D%5E%7Bn%7D%7D[/im]





   

theprophet

#2 Posted 7:42pm 03-02-10  

Re: sqaures

CS kills it at sight
   

Philip

#3 Posted 7:50pm 03-02-10  

Re: sqaures

[im]http://codecogs.izyba.com/gif.latex?Let%20%5C%20%5Cvec%7Ba%7D%3Da_1%5Chat%7Bi%7D+a_2%5Chat%7Bj%7D+a_3%5Chat%7Bk%7D%20%5C%5C%20%5C%20%5C%20and%5C%20%5Cvec%7Bb%7D%3Db_1%5Chat%7Bi%7D+b_2%5Chat%7Bj%7D+b_3%5Chat%7Bk%7D[/im]

u'll notice that [o]a[/o] || [o]b[/o]

[im]http://codecogs.izyba.com/gif.latex?Hence\ %20%5C%3B%20%5C%3B%20%5Cfrac%7Ba_%7B1%7D%5E%7Bn%7D+a_%7B2%7D%5E%7Bn%7D+a_%7B3%7D%5E%7Bn%7D%7D%7Bb_%7B1%7D%5E%7Bn%7D+%20b_%7B2%7D%5E%7Bn%7D+b_%7B3%7D%5E%7Bn%7D%7D=2^{-n}[/im]
The map is not the territory.    

Philip

#4 Posted 7:51pm 03-02-10  

Re: sqaures

@ sir : CS -- Counter Strike ??

didnt get ?

anyways i think my soln is okay....
but pls tell your method
The map is not the territory.    

Philip

#5 Posted 7:55pm 03-02-10  

Re: sqaures

Oh if it is Cauchy schwarz that you meant then Im ok even without seeing that soln...
The map is not the territory.    

Anirudh

#6 Posted 8:43pm 03-02-10  

Re: sqaures

yeah . thanks for the solutions.
   

abhishek93

#7 Posted 5:40pm 22-02-10  

Re: sqaures

plz explain!
   

Nishant

#8 Posted 03:51am 24-02-10  

Re: sqaures

if you noticed, philip you used the proof of CS [6]
-when spring comes, it melts the snow one flake at a time…    

virang1

#9 Posted 09:09am 24-02-10  

Re: sqaures

is CS there for jee?
   

virang1

#10 Posted 09:09am 24-02-10  

Re: sqaures

Can you explain properly how did u do the question.
   

Philip

#11 Posted 11:30pm 24-02-10  

Re: sqaures

@Nishant Bhaiyya : yes, I noticed just after i wrote that this could be a nice proof for CS.  atleast in exact such form for three variables.

However i think it could be extended to any number of variables by induction.

The thought of extending such a nice one by induction was definitely not as satisfying ..so i had a vague idea that something like an n-dimensional vector should exist and sure enough (as i came to know some time later) it does.
The map is not the territory.    
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