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(, Sun 1 Apr 2001, 1:00)
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if xy=1 what is the value of: 2(x+y)^2/2 (x-y)^2 ?

(, Thu 20 Dec 2012, 15:36, 1 reply, 13 years ago)
1

(, Thu 20 Dec 2012, 15:44, Reply)
I made it 16.

(, Thu 20 Dec 2012, 15:46, Reply)
nonce

(, Thu 20 Dec 2012, 15:47, Reply)
If you expand it you get.
2x^2+2xy+2y^2
2x^2-2xy-2y^2

which I think cancels down to either 1 or -1
(, Thu 20 Dec 2012, 15:48, Reply)
But
2^(x+y)^2/2^(x-y)^2 = (2^(-2)^2)/2^(-1 - (-1) )^2 = 16/1 = 16.
(, Thu 20 Dec 2012, 15:49, Reply)
That's if x and y = 1 not if xy=1

(, Thu 20 Dec 2012, 15:51, Reply)
Ah. Yes.
You win.
(, Thu 20 Dec 2012, 15:52, Reply)
Only if it's actually 2^(x+y)^2/2^(x-y)^2

(, Thu 20 Dec 2012, 15:58, Reply)
As explained in my* post at
www.manhattangmat.com/forums/if-xy-1-what-is-the-value-of-2-x-y-2-2-x-y-2-t2912.html

*you can't prove it isn't
(, Thu 20 Dec 2012, 16:00, Reply)

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