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What is the value of x-y?

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What is the value of x-y? [#permalink] New post 29 May 2007, 05:19
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

60% (01:31) correct 40% (05:47) wrong based on 5 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
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 [#permalink] New post 29 May 2007, 06:11
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 :)
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 [#permalink] New post 29 May 2007, 11:07
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.
:-D
  [#permalink] 29 May 2007, 11:07
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