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# x not equal to 0 x=sqrt(4xy-4y^2) then in terms of y, x= a)

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Director
Joined: 06 Feb 2006
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x not equal to 0 x=sqrt(4xy-4y^2) then in terms of y, x= a) [#permalink]

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21 Feb 2006, 12:07
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x not equal to 0 x=sqrt(4xy-4y^2) then in terms of y, x=

a) 2y
b) y
c) y/2
d) -4y^2/(1-2y)
e) -2y
Manager
Joined: 16 Sep 2005
Posts: 62
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21 Feb 2006, 12:15
1
KUDOS
SimaQ wrote:
x not equal to 0 x=sqrt(4xy-4y^2) then in terms of y, x=

a) 2y
b) y
c) y/2
d) -4y^2/(1-2y)
e) -2y

I would go with A (2Y). Explaination as follows.
Given: x=sqrt(4xy-4y^2) and X <> 0
Squaring both the sides of the equation we get
X^2 = 4XY -4Y^2
So X^2 - 4XY + 4Y^2 = 0
Solving this equation we get
(2Y - X)(2Y - X) = 0
So X = 2Y

I hope this makes sense
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Senior Manager
Joined: 11 Jan 2006
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Location: Chennai,India
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21 Feb 2006, 22:30
me to A , but i tried back tracking.. substituted the values from the answers in the equation and only A solved

x = 2y , then from the stem x^2 = 4xy-4y^2 , if x=2y then
4y^2 = 4(2y)y - 4y^2= 8y^2-4y^2=4y^2

thus proved
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21 Feb 2006, 22:33
x^2 = 4xy - 4y^2
x^2 - 4xy + 4y^2 = 0
(x-2y)^2 = 0
x = 2y
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