Find the ratio a/b.

@rengaraj-89Rrct • Oct 14, 2024

Oct 14, 2024

960

Sir / madam,
My question is

The arithmetic mean of two positive numbers a and b is equal to twice their geometric mean. Find the ratio a/b.

Advance Thanks,
R.Rengaraj

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sfdgfdh

@sfdgfdh-aUJpNp • Dec 25, 2009

rengaraj
Sir / madam,
My question is

The arithmetic mean of two positive numbers a and b is equal to twice their geometric mean. Find the ratio a/b.

Advance Thanks,
R.Rengaraj
The arithmetic mean of two positive numbers a and b is equal to twice their geometric mean. Find the ratio a/b.
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Hussanal Faroke

@hussanal-faroke-U5nNM8 • Dec 25, 2009

(a+b)/2 = 2*root(ab)
(a+b)=4*root(ab)
sqr(a+b)=16ab..................................(1)
sqr(a+b)-sqr(a-b)=2ab-(-2ab)
=4ab
ie, sqr(a-b)+4ab= sqr(a+b)
=16ab [:-eq(1)]
sqr(a-b) = 12ab ....................(2)

(2)/(1) sqr(a+b)/sqr(a-b) = 16ab/12ab
=4/3
find square root of both side
(a+b)/(a-b) = +,- 2/root(3)
if 2/root(3),
2a-2b = root(3)a +root(3)b
(2-root(3))a =(2+root(3))b
a/b=(2+root(3))/(2-root(3))

find the result for negtive root urself, i think above proof is correct. if any mistake u find pls inform me! my id: #-Link-Snipped-#

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rengaraj

@rengaraj-89Rrct • Jan 15, 2010

Dear Faroke,
You gave a brilliant solution.
Thanks,
R.Rengaraj
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