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# What is the value of x-y?

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Intern
Joined: 12 May 2007
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What is the value of x-y? [#permalink]  29 May 2007, 05:19
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Difficulty:

(N/A)

Question Stats:

67% (01:39) correct 33% (05:47) wrong based on 3 sessions
I am struggling with this one. Any Help?

What is the value of x-y?

1) x=y+3
2) x^2-2xy+y^2=9

I get the answer somewhat, but statement #2 is confusing me bc I though that sqrt(9) = POSITIVE 3 only, not +3 or -3. Because once you factor out the statement and get (x-y)(x-y)=9 --> (x-y)^2=9, the answer says by squaring both sides you get two possible solutions, x-y=3 and x-y=-3, but isnt the sqrt of both sides leaving you with x-y=+3 bc its only a positive root? Any ideas on this one this whole sqroot + versus - business? Thanks
SVP
Joined: 01 May 2006
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It's (A)

Why not (D)?
o Sqrt(x^2-2xy+y^2) = Sqrt( (x-y)^2) = |x-y|

So, |x-y| = 3 <=> x-y = 3 or x-y = -3

This is one way to figure it out and to remember it
Intern
Joined: 22 Mar 2007
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Thanks Fig ,nice logic

and dear americo

you can imagine (x-y) as just one variable like Z so

(Z)^2=9 then z can be +3 or -3. and the question asks for value of x-y.

although Fig's explanation is much better but may be its another way of thinking about it.
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