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# If x^2 + y^2 = xy, then (x + y)^4 =

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Math Expert
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If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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31 May 2017, 00:45
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Question Stats:

67% (01:07) correct 33% (01:14) wrong based on 87 sessions

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If $$x^2 + y^2 = xy$$, then $$(x + y)^4 =$$

(A) $$xy$$

(B) $$x^2*y^2$$

(C) $$9x^2*y^2$$

(D) $$(x^2 + y^2)^2$$

(E) $$x^4 + y^4$$
[Reveal] Spoiler: OA

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Re: If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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31 May 2017, 01:04
C.
Add 2xy on both sides and rhs side becomes (a+b)^2

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Re: If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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31 May 2017, 03:06
Given: x^2 + y^2 = xy
If we add 2xy to both sides, we get: x^2 + y^2 + 2xy = 3xy Or (x+y)^2 = 3xy

Now, (x+y)^4 = [(x+y)^2]^2 = (3xy)^2 = 9 * x^2 * y^2

Hence option C
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Re: If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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01 Jun 2017, 16:28
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Bunuel wrote:
If $$x^2 + y^2 = xy$$, then $$(x + y)^4 =$$

(A) $$xy$$

(B) $$x^2*y^2$$

(C) $$9x^2*y^2$$

(D) $$(x^2 + y^2)^2$$

(E) $$x^4 + y^4$$

We are given:

x^2 + y^2 = xy.

Note that (x + y)^4 = [(x + y)^2]^2 = [x^2 + 2xy + y^2]^2.

Since x^2 + y^2 = xy,

[x^2 + 2xy + y^2]^2 = [2xy + xy]^2 = (3xy)^2 = 9(x^2)(y^2).

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Re: If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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28 Aug 2017, 00:13
1
KUDOS

I am getting C
Math Expert
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Posts: 43785
Re: If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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28 Aug 2017, 00:56
hanyhamdani wrote:

I am getting C

The correct answer is C. Edited. Thank you.
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Re: If x^2 + y^2 = xy, then (x + y)^4 = [#permalink]

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28 Aug 2017, 01:53
x^2+y^2 = xy
(x+y)^2 = x^2 + y^2 + 2xy = xy +2xy =3xy
(x+y)^4= (3xy)^2= 9x^2. y^2
option C
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Re: If x^2 + y^2 = xy, then (x + y)^4 =   [#permalink] 28 Aug 2017, 01:53
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