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# If 2x^2 - y^2 = 2xy, then (x+y)^2 =

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If 2x^2 - y^2 = 2xy, then (x+y)^2 = [#permalink]

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10 May 2010, 17:45
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Question Stats:

73% (02:22) correct 27% (02:19) wrong based on 439 sessions

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If 2x^2 - y^2 = 2xy, then (x+y)^2 =

A. x^2
B. 3x^2
C. 4xy
D. 2y^2
E. -y^2
[Reveal] Spoiler: OA

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10 May 2010, 17:50
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Its B

2x^2 -y^2 = 2xy
2x^2 = 2xy + y^2

Add x^2 on both sides we get

2x^2 +x^2 = x^2 +y^2 +2xy
3x^2 = (x+y)^2
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10 May 2010, 17:53
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Expert's post
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bakfed wrote:
If 2x^2 - y^2 = 2xy, then (x+y)^2 =

A. x^2
B. 3x^2
C. 4xy
D. 2y^2
E. -y^2

OA
[Reveal] Spoiler:
B

Given: $$2xy=2x^2-y^2$$.

$$(x+y)^2 =x^2+2xy+y^2$$ --> substitute $$2xy$$ --> $$(x+y)^2 =x^2+(2x^2 - y^2)+y^2=3x^2$$.

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18 May 2010, 09:17
1
KUDOS
bakfed wrote:
If 2x^2 - y^2 = 2xy, then (x+y)^2 =

A. x^2
B. 3x^2
C. 4xy
D. 2y^2
E. -y^2

OA
[Reveal] Spoiler:
B

here we have to find the value of x^2 +y^2 +2xy in which 2xy
=2x^2 -y^2 (given ) hence ans is 3x^2.
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Re: If 2x^2 - y^2 = 2xy, then (x+y)^2 = [#permalink]

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03 Nov 2014, 05:03
Hello from the GMAT Club BumpBot!

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Re: If 2x^2 - y^2 = 2xy, then (x+y)^2 = [#permalink]

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10 Apr 2016, 06:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 2x^2 - y^2 = 2xy, then (x+y)^2 = [#permalink]

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24 Mar 2017, 05:30
Quite straight forward question

step 1:
(x+Y)^2 = X^2 +2xy + y^2

step 2:
now substitute 2xy from the equation.

(x+Y)^2 = X^2 +2x^2-y^2+y^2.

-y^2 and Y^2 cancels out

we are left with x^2+2X^2= 3X^2 Hence B.
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Re: If 2x^2 - y^2 = 2xy, then (x+y)^2 = [#permalink]

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27 Mar 2017, 17:22
1
KUDOS
Expert's post
bakfed wrote:
If 2x^2 - y^2 = 2xy, then (x+y)^2 =

A. x^2
B. 3x^2
C. 4xy
D. 2y^2
E. -y^2

We see that we are looking for the value of (x + y)^2 = x^2 + y^2 + 2xy.

We also see that 2x^2 - y^2 = 2xy; thus we can substitute for 2xy and we have:

x^2 + y^2 + 2x^2 - y^2 = 3x^2

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Re: If 2x^2 - y^2 = 2xy, then (x+y)^2 = [#permalink]

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24 Apr 2017, 20:38
bakfed wrote:
If 2x^2 - y^2 = 2xy, then (x+y)^2 =

A. x^2
B. 3x^2
C. 4xy
D. 2y^2
E. -y^2

An efficient way to solve this question is to foil (x + y)^2 and substitute- foiling is critical

X^2 + (2x^2 - y^2) + y^2
Re: If 2x^2 - y^2 = 2xy, then (x+y)^2 =   [#permalink] 24 Apr 2017, 20:38
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