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Algebra
dris's Avatar
dris
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Joined: 20 Oct 2008
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14 Jul 2009 01:38:49 IST
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If (a^n+b^n)/(a^(n-1) + b^(n-1)) is the A.M. between a and b, then find the value of n?
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If (a^n+b^n)/(a^(n-1) + b^(n-1)) is the A.M. between a and b, then find the value of n?


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Mirka
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14 Jul 2009 01:54:34 IST
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n = 1

 
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dris
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14 Jul 2009 02:36:14 IST
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b4 the statement if a is nt = b cud u explain the statement ?
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edison
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14 Jul 2009 10:37:42 IST
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Very nicely replied.

However if a = b then the AM will be same as a and b i.e.

AM = a = b

This can be seen by simplifying the expression as below

 

AM = (an + bn ) / (an-1 + bn-1)

 

or AM = 2(an) / (2an-1)              [ as a = b]

 

or AM = a
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Mirka
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14 Jul 2009 23:55:27 IST
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@ dris :

 

hope its clear now !
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dris
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15 Jul 2009 00:30:31 IST
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yeah i got it but cud u tell why di u take n-1=0 .
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Mirka
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15 Jul 2009 01:06:03 IST
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that's becoz anything power zero is 1, except when this "anything" is zero or infinity. so here a/b power n-1 = 1 , so n-1 = 0 or n = 1
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