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# If x^2 + 2xy + y^2 = 25, then (x + y)^3 could be

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If x^2 + 2xy + y^2 = 25, then (x + y)^3 could be [#permalink]  21 Jun 2017, 02:21
Expert's post
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Question Stats:

87% (00:33) correct 12% (00:00) wrong based on 8 sessions

If $$x^2$$ + 2xy + $$y^2$$ = 25, then $$(x + y)^3$$ could be

A) 5

B) 15

C) 50

D) 75

E) 125
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
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Kudos [?]: 1113 [1] , given: 7

Re: If x^2 + 2xy + y^2 = 25, then (x + y)^3 could be [#permalink]  05 Aug 2017, 06:36
1
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Expert's post
Carcass wrote:

If $$x^2$$ + 2xy + $$y^2$$ = 25, then $$(x + y)^3$$ could be

A) 5

B) 15

C) 50

D) 75

E) 125

Given: x² + 2xy + y² = 25
Factor to get: (x + y)(x + y) = 25
So: (x + y)² = 25
We can conclude that EITHER x + y = 5 OR x + y = -5

This means that EITHER (x + y)³ = (5)³ = 125 OR (x + y)³ = (-5)³ = -125

[Reveal] Spoiler:
E

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Re: If x^2 + 2xy + y^2 = 25, then (x + y)^3 could be   [#permalink] 05 Aug 2017, 06:36
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