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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

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03 Jul 2013, 01:54

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This post received KUDOS

vintage83 wrote:

If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

A. 0 B. 1 C. 2 D. 5 E. 10

Given that \(x^2 - xy - 10 - 2y^2 = 0 \to x^2+4y^2-4xy-10-xy-2y^2=4y^2-4xy\) [By adding \(4y^2\) and \(4xy\) on both sides]\(\to\) \((x-2y)^2 = 6y^2-3xy+10\)

Or \((x-2y)^2 = 3y(2y-x)+10 \to (x-2y)^2+3y(x-2y) = 10\to (x-2y)(x-2y+3y) = 10 \to (x-2y) = \frac{10}{x+y}\) = 5. D.
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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

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18 Aug 2015, 17:43

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Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

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22 Nov 2015, 10:19

oh man..tricky one..I couldn't see the short way to solve it:

(x+y) = 2 and (x+y)^2 = 4 multiply the second equation by 2 and get: 2x^2 -2xy-20-4y^2 = 0 now add 2 equations 2x^2 -2xy-20-4y^2 = 0+ x^2 +2xy +y^2 = 4

we get: 3x^2 -20 - 3y^2 = 4 or 3x^2 - 3y^2 = 24 divide by 3: x^2 - y^2 = 8 rewrite the equation: (x+y)(x-y) = 8 we have x+y = 2, that means x-y = 4 x=4+y

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