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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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11 Nov 2010, 21:38
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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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Re: If 2x^2 –y^2 = 2xy [#permalink]

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11 Nov 2010, 23:21
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monirjewel 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

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

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Re: If 2x^2 –y^2 = 2xy [#permalink]

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12 Nov 2010, 13:46
2x^2 –y^2 = 2xy
2x^2 = 2xy+y^2

3x^2 = x^2 + 2xy+y^2 (adding x^2 on both sides)

3x^2 = (x+y)^2

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Re: If 2x^2 –y^2 = 2xy [#permalink]

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12 Nov 2010, 16:30
2x$$^2$$-y$$^2$$=2xy

(x+y)$$^2$$= x$$^2$$+2xy+y$$^2$$

replace 2xy by 2x$$^2$$-y$$^2$$ and solve

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Re: If 2x^2 –y^2 = 2xy [#permalink]

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29 Dec 2010, 12:08
Sarang wrote:
2x^2 –y^2 = 2xy
2x^2 = 2xy+y^2

3x^2 = x^2 + 2xy+y^2 (adding x^2 on both sides)

3x^2 = (x+y)^2

i didn't understand this pls explain
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Re: If 2x^2 –y^2 = 2xy [#permalink]

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29 Dec 2010, 12:33
rahul321 wrote:
Sarang wrote:
2x^2 –y^2 = 2xy
2x^2 = 2xy+y^2

3x^2 = x^2 + 2xy+y^2 (adding x^2 on both sides)

3x^2 = (x+y)^2

i didn't understand this pls explain

Given: $$2x^2-y^2=2xy$$ --> rearrange: $$2x^2=2xy+y^2$$ --> add $$x^2$$ to both parts of the equation: $$2x^2+x^2=x^2+2xy+y^2$$ --> $$3x^2=(x+y)^2$$.

Hope it's clear.
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If 2x^2 –y^2 = 2xy, then (x+y)^2= [#permalink]

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17 Jul 2014, 01:42
$$2x^2 – y^2 = 2xy$$

so, $$y^2 = 2x^2 - 2xy$$ ............ (1)

$$(x+y)^2 = x^2 + 2xy + y^2$$

Placing value of $$y^2$$ from (1)

$$= x^2 + 2xy + 2x^2 - 2xy$$

$$= 3x^2$$

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

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20 Jul 2015, 19:33
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Re: If 2x^2 –y^2 = 2xy, then (x+y)^2= [#permalink]

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21 Jul 2015, 07:38
$$2x^2 - y^2 = 2xy$$

$$(x+y)^2 = x^2 + 2xy + y^2 = x^2 + 2x^2 - y^2 + y^2 = 3x^2$$. Ans (B).
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Re: If 2x^2 –y^2 = 2xy, then (x+y)^2= [#permalink]

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31 Aug 2016, 10:27
Hello from the GMAT Club BumpBot!

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Re: If 2x^2 –y^2 = 2xy, then (x+y)^2=   [#permalink] 31 Aug 2016, 10:27
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