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

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink]  23 Jun 2018, 11:49
Expert's post
00:00

Question Stats:

86% (00:41) correct 13% (01:12) wrong based on 23 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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Sandy
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Intern
Joined: 05 Jan 2018
Posts: 32
Followers: 0

Kudos [?]: 20 [0], given: 8

Re: If x + y = –3 and x2 + y2 = 12, what is the value of 2xy? [#permalink]  25 Jun 2018, 07:03
Ans. -3
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 [0], given: 394

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