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if xy=1, what is the value of 2(x+y)^2/2(x-y)^2? A. 2 B. 4

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Senior Manager
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if xy=1, what is the value of 2(x+y)^2/2(x-y)^2? A. 2 B. 4 [#permalink] New post 16 Feb 2007, 16:07
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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
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Re: PS [#permalink] New post 16 Feb 2007, 16:41
buckkitty wrote:
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


Are you sure you copied the question right? 1s cancel off right away, doesnt look right
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Re: PS [#permalink] New post 16 Feb 2007, 18:01
buckkitty wrote:
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


I think you mean 2^((x+y)^2)/2^((x-y)^2)

If this is the case, then

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

2^A/2^B=2^(A-B)

Substitute A and B and you get 2^(4xy)

If xy=1, then the expression becomes 2^4=16.

D.
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Re: PS [#permalink] New post 16 Feb 2007, 20:58
ncprasad wrote:
buckkitty wrote:
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


I think you mean 2^((x+y)^2)/2^((x-y)^2)

If this is the case, then

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


2^A/2^B=2^(A-B)

Substitute A and B and you get 2^(4xy)

If xy=1, then the expression becomes 2^4=16.

D.


this makes sense... the question as it is will not give a numerical solution...
Senior Manager
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 [#permalink] New post 17 Feb 2007, 10:53
no wonder I couldnt solve it. I had this problem written in my error log incorrectly.

as ncprasad correctly pointed out, the question should be as follows:

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
  [#permalink] 17 Feb 2007, 10:53
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if xy=1, what is the value of 2(x+y)^2/2(x-y)^2? A. 2 B. 4

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