x&y algebra

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x&y algebra

by LevelOne » Sun Jun 21, 2009 1:04 pm
If xy=1, what is the value of 2^(x+y)^2/2^(x-y)^2?

A. 2
B. 4
C. 8
D. 16
E. 32

thanks!

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D

by tryingtocrack » Sun Jun 21, 2009 3:00 pm
D

2 ^ 4xy

2 ^ 4 = 16

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by ssmiles08 » Sun Jun 21, 2009 3:16 pm
In a more expanded form:

2^(x+y)^2 = 2^(x^2 + 2xy + y^2)

2^(x-y)^2 = 2^(x^2 - 2xy + y^2)

by dividing you subtract the roots:

x^2 + 2xy + y^2 - (x^2 - 2xy + y^2)

= 4xy

4*1 = 4

2^4 = 16

(D)

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by LevelOne » Mon Jun 22, 2009 12:32 am
ssmiles08, I find your detailed explanation really useful. thanks