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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

Posts: 4805

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]

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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Joined: 05 Jan 2018

Posts: 32

Re: If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink]

25 Jun 2018, 07:03

Ans. -3

sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4805

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]

28 Jul 2018, 16:07

Expert Reply

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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