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# If x<y, and y(y−2x)=2-x^2, what is the value of x−y?

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Intern
Joined: 21 Mar 2013
Posts: 38
GMAT Date: 03-20-2014
If x<y, and y(y−2x)=2-x^2, what is the value of x−y?  [#permalink]

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Updated on: 07 Mar 2014, 01:32
1
9
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:17) correct 43% (01:07) wrong based on 207 sessions

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If x<y, and y(y−2x)=2− x^2, what is the value of x−y?

A) −2

B) −$$\sqrt{2}$$

C) −1

D) 1

E) $$\sqrt{2}$$

Originally posted by idinuv on 07 Mar 2014, 01:28.
Last edited by Bunuel on 07 Mar 2014, 01:32, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: If x<y, and y(y−2x)=2-x^2, what is the value of x−y?  [#permalink]

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07 Mar 2014, 01:37
idinuv wrote:
If x<y, and y(y−2x)=2− x^2, what is the value of x−y?

A) −2

B) −$$\sqrt{2}$$

C) −1

D) 1

E) $$\sqrt{2}$$

$$y(y-2x)=2- x^2$$ --> $$y^2-2xy=2-x^2$$ --> $$y^2-2xy+x^2=2$$ --> $$(x-y)^2=2$$. Since x<y (x-y<0), then $$x-y=-\sqrt{2}$$.

Hope it's clear.
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Re: If x<y, and y(y−2x)=2-x^2, what is the value of x−y?  [#permalink]

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24 Sep 2018, 11:29
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Re: If x<y, and y(y−2x)=2-x^2, what is the value of x−y? &nbs [#permalink] 24 Sep 2018, 11:29
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