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# If 2x + 2y = 1/2x − 2y , then x^2 − y^2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If 2x + 2y = 1/2x − 2y , then x^2 − y^2 =  [#permalink]

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21 Jan 2019, 23:52
00:00

Difficulty:

15% (low)

Question Stats:

83% (00:42) correct 17% (01:28) wrong based on 26 sessions

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If $$2x + 2y = \frac{1}{2x − 2y}$$, then $$x^2 − y^2 =$$

A 1/8
B 1/4
C 1/2
D 1
E 2

_________________
VP
Joined: 31 Oct 2013
Posts: 1163
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If 2x + 2y = 1/2x − 2y , then x^2 − y^2 =  [#permalink]

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22 Jan 2019, 00:02
Bunuel wrote:
If $$2x + 2y = \frac{1}{2x − 2y}$$, then $$x^2 − y^2 =$$

A 1/8
B 1/4
C 1/2
D 1
E 2

Given,

$$2x + 2y = \frac{1}{2x − 2y}$$

(2x + 2y) ( 2x -2y) = 1

$$(2x)^2 -(2y)^2 = 1$$

$$4x^2 - 4y^2 = 1$$

$$4(x^2 - y^2) = 1$$

$$x^2 - y^2 = 1/4.$$

SVP
Joined: 18 Aug 2017
Posts: 1928
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 2x + 2y = 1/2x − 2y , then x^2 − y^2 =  [#permalink]

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22 Jan 2019, 02:59
Bunuel wrote:
If $$2x + 2y = \frac{1}{2x − 2y}$$, then $$x^2 − y^2 =$$

A 1/8
B 1/4
C 1/2
D 1
E 2

solve the given eqn
we get
$$x^2 − y^2 =$$ = 1/4
IMO B
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VP
Joined: 09 Mar 2018
Posts: 1003
Location: India
If 2x + 2y = 1/2x − 2y , then x^2 − y^2 =  [#permalink]

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22 Jan 2019, 03:20
Bunuel wrote:
If $$2x + 2y = \frac{1}{2x − 2y}$$, then $$x^2 − y^2 =$$

A 1/8
B 1/4
C 1/2
D 1
E 2

IMO B

If $$2x + 2y = \frac{1}{2x − 2y}$$

So, i prefer solving the if part first

$$(2x + 2y) (2x-2y) = 1$$

Take out 2 common from both the expressions and use this $$(x + y) (x-y) = x^2 - y^2$$

$$2* 2 * x^2 - y^2 = 1$$

$$x^2 - y^2 = 1/4$$
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If 2x + 2y = 1/2x − 2y , then x^2 − y^2 =   [#permalink] 22 Jan 2019, 03:20
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