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If x + y = –3 and x2 + y2 = 12, what is the value of 2xy?

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink] New post 23 Jun 2018, 11:49
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Question Stats:

77% (00:56) correct 22% (01:48) wrong based on 9 sessions
If \(x + y = -3\) and \(x^2 + y^2 = 12\), what is the value of \(2xy\)?

[Reveal] Spoiler: OA
-3

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Re: If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink] New post 25 Jun 2018, 07:03
Ans. -3
GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1899 [0], given: 397

Re: If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink] New post 28 Jul 2018, 16:07
Expert's post
Explanation

One of the “special products” you need to memorize for the GRE is \(x^2 + 2xy + y^2 = (x + y)^2\).

Write this pattern on your paper, plug in the given values, and simplify, solving for 2xy:

\(x^2 + 2xy + y^2 = (x + y)^2\)
\((x^2 + y^2) + 2xy = (x + y)^2\)
\((12) + 2xy = (–3)^2\)
\(12 + 2xy = 9\)
\(2xy = –3\)
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Re: If x + y = –3 and x2 + y2 = 12, what is the value of 2xy?   [#permalink] 28 Jul 2018, 16:07
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If x + y = –3 and x2 + y2 = 12, what is the value of 2xy?

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