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What is the value of [m]x^2 + y^2[/m] ?

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What is the value of [m]x^2 + y^2[/m] ? [#permalink] New post 26 Aug 2012, 08:56
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22% (03:24) correct 78% (01:21) wrong based on 9 sessions
What is the value of x^2 + y^2 ?
(1) x^2 + y^2 = 2xy + 1
(2) x^2 + y^2 = 4 - 2xy

I don't agree with the OA.
If we add (1) and (2):

(1) x^2 -2xy + y^2 = 1
(2) x^2 +2xy+ y^2 = 4
-------------------------------------
Total: 2x^2 +2y^2 = 5

Then: x^2 + y^2 = \frac{5}{2}

Please, your comments.
[Reveal] Spoiler: OA

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Re: What is the value of [m]x^2 + y^2[/m] ? [#permalink] New post 26 Aug 2012, 09:41
Expert's post
When trying to solve for x and y, it doesn't appear that we can find a solution for x^2 + y^2
2xy + 1 = 4 - 2xy

4xy = 3
xy = 3/4

However, the approach of canceling out 2xy DOES remove the xy variable and leaves us cleanly with x^2 + y^2. We indeed have the value as you mentioned...perhaps the source for the OA is incorrect.
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Re: What is the value of [m]x^2 + y^2[/m] ?   [#permalink] 26 Aug 2012, 09:41
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What is the value of [m]x^2 + y^2[/m] ?

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