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AM-GM problem
Posted: Sat Dec 18, 2010 10:37 am
by rakeen
Kulna08-hisec-Q6
the AM(arithmetic mean) of x and y is a. and GM(geometric mean) is g. if a+g = y-x then what is $\frac{x}{y}$
Re: AM-GM problem
Posted: Sun Dec 19, 2010 2:06 pm
by AntiviruShahriar
Re: AM-GM problem
Posted: Sun Dec 19, 2010 7:10 pm
by rakeen
ki hoilo? ektu bistarito bolba. r ami bangla likhle bangla dekhte pai na keno? avro use kortesi and amar bangla font use kora ase. Jokhon Bijoy chilo tokhon thik motoi avro cholte silo. But bijoy uninstall korar pore avro te bangla use korle ta dekhte pai na.(box ashe)
Re: AM-GM problem
Posted: Mon Dec 20, 2010 1:07 pm
by AntiviruShahriar
$a+g=y-x$
$\frac{x+y+2\sqrt{xy}}{2}=y-x$
$(9x-y)(x-y)=0$
if $x=y$ then 1st line is wrong...........s_____
avror bepare onno vaiara valoo bolte parbe
Re: AM-GM problem
Posted: Mon Dec 20, 2010 1:29 pm
by rakeen
how did u get (9x-y)(x-y) = 0
Re: AM-GM problem
Posted: Mon Dec 20, 2010 2:32 pm
by AntiviruShahriar
rakeen wrote:how did u get (9x-y)(x-y) = 0
after the 2nd line of my last post::::
$\sqrt{xy} =\frac{y-3x}{2}$
$4xy=y^2-6xy+9x^2$
$(9x-y)(x-y)=0$
if $x=y$ then $a+g =y-x$ line is wrong...........
so $\frac{x}{y}=\frac{1}{9}$
Re: AM-GM problem
Posted: Tue Dec 21, 2010 11:32 pm
by Dipan
Thanks to rakeen and anti...I have got a huge benefit from this two mathematicians(pam)
Re: AM-GM problem
Posted: Fri Aug 12, 2011 1:30 am
by tanzad
Bismillahir Rahmanir Raheem.
If x=y then is a+g=y−x wrong?
What about x=y=0?
(0+0)/2 + sqrt(0*0) = 0-0.
Tanvir Zawad
Re: AM-GM problem
Posted: Sun Sep 04, 2011 1:23 pm
by ibrahim
AM bujhi, GM ta keo bujhaya diba?
Re: AM-GM problem
Posted: Sun Sep 04, 2011 1:26 pm
by ibrahim
AM bujhi, GM ta keo bujhaya diba?
akashe shurjota uthe nirobe