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

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Math Expert
Joined: 02 Sep 2009
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If x^2 + y^2 = xy, then (x + y)^4 =  [#permalink]

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Updated on: 09 Jul 2019, 04:06
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:20) correct 26% (01:31) 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) $$x^4 + y^4$$

Source: Nova GMAT
Difficulty Level: 600

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Originally posted by Bunuel on 31 May 2017, 01:45.
Last edited by SajjadAhmad on 09 Jul 2019, 04:06, edited 1 time in total.
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Re: If x^2 + y^2 = xy, then (x + y)^4 =  [#permalink]

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31 May 2017, 02:04
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, 04:06
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, 17:28
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, 01:13
1

I am getting C
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Posts: 59590
Re: If x^2 + y^2 = xy, then (x + y)^4 =  [#permalink]

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28 Aug 2017, 01:56
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, 02:53
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]

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24 Mar 2019, 20:53
We have:

$$x^2 + y^2 = xy$$

$$(x + y)^2 = 3xy$$

So

$$((x + y)^2)^2) = (3xy)^2$$

C
Re: If x^2 + y^2 = xy, then (x + y)^4 =   [#permalink] 24 Mar 2019, 20:53
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