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What is the value of xy ?

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Junior | Next Rank: 30 Posts
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by expert » Sat Apr 11, 2009 2:54 pm
Hi guys. Could you please explain how to solve ?
What is the value of xy ?

(1) (x + y)^2 = 37
(2) (x - y)^2 = 17
I can see that (1) and (2) alone are insufficient. If I solve (1) AND (2) I get following results (or numeric roots here):

Image

Since it has more than one root I answered E.

Thanks!
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by vittalgmat » Sat Apr 11, 2009 3:10 pm
IMO C.

Here is how I approached.

Stmts 1 and 2 independently are insufficient.

So could be C or E.
Lets look at them together.

expand both stmts.

x^2 +2xy +y^2 = 37 -------(1)
x^2 -2xy +y^2 = 17 ---------(2)

Multiply (2) by -1 and add to (1).
the square terms will cancel out giving us
4xy = 20
xy = 5.

So C.

Ht Helps
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by cramya » Sat Apr 11, 2009 3:37 pm
Well done Vittal!

(1) - (2) gives us the same

4xy = 20
xy=5
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by expert » Sat Apr 11, 2009 3:39 pm
Thank you, vittalgmat! It's so simple!
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