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What is the value of x^2 + y^2 ?

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What is the value of x^2 + y^2 ? [#permalink]

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New post 04 Oct 2010, 18:06
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What is the value of \(x^2 + y^2\)?

1. \(x^2 + y^2 = 2xy + 1\)
2. \(x^2 + y^2 = 4 - 2xy\)

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-2-y-142923.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Nov 2014, 01:45, edited 1 time in total.
Edited the OA.

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Re: What is the value of x^2 + y^2 ? [#permalink]

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New post 04 Oct 2010, 18:51
1) it's given in terms of xy, insufficient

2) again same problem, insufficient

1+2) add together the equations and divide by 2. X^2+y^2=2.5
sufficient

Answer is (c)

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Re: What is the value of x^2 + y^2 ? [#permalink]

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New post 04 Oct 2010, 19:34
shrouded1 wrote:
1) it's given in terms of xy, insufficient

2) again same problem, insufficient

1+2) add together the equations and divide by 2. X^2+y^2=2.5
sufficient

Answer is (c)

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Yup I get the same thing.. OA must be wrong

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Re: What is the value of x^2 + y^2 ? [#permalink]

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New post 04 Oct 2010, 20:37
Yes.. I get C too.. OA must be wrong..
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Re: What is the value of x^2 + y^2 ? [#permalink]

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New post 16 Oct 2010, 07:14
shd be C according to me as well...

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Re: What is the value of x^2 + y^2 ? [#permalink]

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New post 23 Nov 2014, 08:50
I also end up with C.

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Re: What is the value of x^2 + y^2 ? [#permalink]

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New post 24 Nov 2014, 01:45
krazo wrote:
What is the value of \(x^2 + y^2\)?

1. \(x^2 + y^2 = 2xy + 1\)
2. \(x^2 + y^2 = 4 - 2xy\)


What is the value of x^2+y^2 ?

(1) x^2+y^2=2xy+1 --> \(x^2-2xy+y^2=1\) --> \((x-y)^2=1\). If \(x=1\) and \(y=0\), then \(x^2+y^2=1\) but if \(x=2\) and \(y=1\), then \(x^2+y^2=5\). Not sufficient.

(2) x^2+y^2=4-2xy --> \(x^2+2xy+y^2=4\) --> \((x+y)^2=4\). If \(x=2\) and \(y=0\), then \(x^2+y^2=4\) but if \(x=1\) and \(y=1\), then \(x^2+y^2=2\). Not sufficient.

(1)+(2) Sum the equations: \(2(x^2+y^2)=5\) --> \(x^2+y^2=2.5\). Sufficient.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-2-y-142923.html
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Re: What is the value of x^2 + y^2 ?   [#permalink] 24 Nov 2014, 01:45
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