AM-GM problem
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
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 $\frac{x}{y}$
the AM(arithmetic mean) of x and y is a. and GM(geometric mean) is g. if a+g = y-x then what is $\frac{x}{y}$
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Re: AM-GM problem
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Re: AM-GM problem
$a+g=y-x$
$\frac{x+y+2\sqrt{xy}}{2}=y-x$
$(9x-y)(x-y)=0$
if $x=y$ then 1st line is wrong...........s_____
avror bepare onno vaiara valoo bolte parbe
$\frac{x+y+2\sqrt{xy}}{2}=y-x$
$(9x-y)(x-y)=0$
if $x=y$ then 1st line is wrong...........s_____
avror bepare onno vaiara valoo bolte parbe
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- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
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Re: AM-GM problem
after the 2nd line of my last post::::rakeen wrote:how did u get (9x-y)(x-y) = 0
$\sqrt{xy} =\frac{y-3x}{2}$
$4xy=y^2-6xy+9x^2$
$(9x-y)(x-y)=0$
if $x=y$ then $a+g =y-x$ line is wrong...........
so $\frac{x}{y}=\frac{1}{9}$
Re: AM-GM problem
Thanks to rakeen and anti...I have got a huge benefit from this two mathematicians(pam)
Re: AM-GM problem
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
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
AM bujhi, GM ta keo bujhaya diba?
Re: AM-GM problem
AM bujhi, GM ta keo bujhaya diba?
akashe shurjota uthe nirobe
akashe shurjota uthe nirobe