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If x is an integer

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Source: — Data Sufficiency |
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Re: If x is an integer

by piyush_nitt » Tue Mar 03, 2009 5:39 am
jfranco23 wrote:If x is an integer, is (9^x) + (9^-x) = b?

1. (3^x) + (3^-x) = root(b+2)
2. x>0
IMO A

1. (3^x) + (3^-x) = root(b+2)
squaring both sides

(3^x)^2 + (3^-x)^2 + 2 = b+2
9^x + 9^-x = b

Hence A is SUFF

2. NOT SUFF

don't know any relation between x and b
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by jfranco23 » Tue Mar 03, 2009 5:44 am
How did you get the "+ 2" of the left side?
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by piyush_nitt » Tue Mar 03, 2009 5:50 am
jfranco23 wrote:How did you get the "+ 2" of the left side?
(a+b)^2 = a^2 + b^2 + 2ab

Here

(3^x + 3^-x)^2 = (3^x)^2 + (3^-x)^2 + 2 (3^x) (3^-x)

3^x * 3^-x = 1

Therefore 2 (3^x) (3^-x) = 2
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