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If x + y = –3 and x2 + y2 = 12, what is the value of 2xy?
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sandy
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
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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If \(x + y = -3\) and \(x^2 + y^2 = 12\), what is the value of \(2xy\)?

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kinal30
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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
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sandy
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Posts: 4804
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink] New post  28 Jul 2018, 16:07
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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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