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Algebra

Cool goIITian

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4 Mar 2010 17:05:37 IST

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474

Another progressions question. plz ans fast.

None

Find the value of n so that

(a^(n+1) +b^(n+1))/(a^n + b^n)

is the geometric mean between a and b.

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Comments (5)

sravan

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Joined: 21 Sep 2008

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4 Mar 2010 17:30:27 IST

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answer is -1/2

sravan

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4 Mar 2010 17:40:05 IST

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answer is -1/2

Hari Shankar

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Joined: 28 Feb 2007

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5 Mar 2010 14:47:07 IST

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$\frac{a^{n+1} + b^{n+1}}{a^n+b^n} = \sqrt{ab}$

Putting x = a/b, the equation becomes:

$\frac{x^{n+1} + 1}{x^n+1} = \sqrt{x}$

or $x^{n+1} + 1 =x^{n + \frac{1}{2}}+\sqrt x$

or $x^{n+\frac{1}{2}}(\sqrt x-1) = \sqrt x-1$

or $x^{n+\frac{1}{2}}=1 \Rightarrow n = -\frac{1}{2}$

ayush

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Joined: 9 Mar 2008

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5 Jul 2010 12:42:17 IST

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SIR answer is right but how can we n=-1/2

n can't be negative .

Hari Shankar

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5 Jul 2010 14:13:10 IST

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Where does it say so?

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