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Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y

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Manager
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Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post 26 Nov 2007, 10:50
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Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)

(2) x = y
SVP
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 [#permalink] New post 26 Nov 2007, 10:59
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)

(2) x = y

is

x(x-y) = 0 ie: is x = 0 or y = x

from one
(x-y)(x+y) = (x+5)(y-5) = [(x-(-5)) ((-5) +y)] ie: x = -5,y = -5 ie x = y

suff

from2

x=y still ..SUFF

my answer is d
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 [#permalink] New post 26 Nov 2007, 12:40
Thats what i thought too, but apparently the OA is not D. Just wondering why..
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 [#permalink] New post 26 Nov 2007, 13:29
Expert's post
B.

1. x^2 – y^2 = (x + 5)(y - 5)=xy+5y-5x-25
x^2 – y^2 -xy-5y+5x+25=0
x^2 + (5-y)x + (25–y^2-5y)=0

we can put for example 4 or 3 instead y and obtain different x.
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 [#permalink] New post 16 Dec 2007, 15:03
any other folks want to take a shot at this one ?
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 [#permalink] New post 16 Dec 2007, 15:25
yezz wrote:

(x-y)(x+y) = (x+5)(y-5) = [(x-(-5)) ((-5) +y)] ie: x = -5,y = -5 ie x = y



A possible reason why this doesn't hold is that if you go back and put -5 into the equation you then zero the equation on both sides which you can't do.

In other words
(x+5)=-5+5=0 this is not a valid solution and you cannot then prove the value of y.
  [#permalink] 16 Dec 2007, 15:25
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