Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 21 May 2013, 03:13

# If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2

Author Message
TAGS:
Manager
Joined: 07 Feb 2011
Posts: 88
Followers: 0

Kudos [?]: 4 [0], given: 43

If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2 [#permalink]  25 May 2012, 15:14
00:00

Question Stats:

66% (02:11) correct 33% (02:20) wrong based on 0 sessions
If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2y^2, which of the following could be the value of x2 in terms of y?

A. 4y^2/3
B. 2y^2
C. (2y^2+1)/3
D. 2y^2
E. 6y^2/3

When a problem involves variables raised to the fourth power, it is often useful to represent them as a square of another square, since this approach will allow us to apply manipulations of squares. Also note that since we are dealing with high exponents, the approach of plugging numbers would prove time-consuming and prone to error in this case.

9x4 – 4y4 = (3x2)2 – (2y2)2 = (3x2 + 2y2)(3x2 – 2y2).

(3x2 + 2y2)(3x2 – 2y2) = (3x2 + 2y2)

I'm not getting how (3x2 + 2y2)(3x2 – 2y2) = (3x2 + 2y2). Can someone please explain?
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 25 May 2012, 15:22, edited 1 time in total.
Edited the question and moved to PS subforum
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11532
Followers: 1795

Kudos [?]: 9552 [0], given: 826

Re: If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2 [#permalink]  25 May 2012, 15:32
manimgoindowndown wrote:
If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2y^2, which of the following could be the value of x2 in terms of y?

A. 4y^2/3
B. 2y^2
C. (2y^2+1)/3
D. 2y^2
E. 6y^2/3

When a problem involves variables raised to the fourth power, it is often useful to represent them as a square of another square, since this approach will allow us to apply manipulations of squares. Also note that since we are dealing with high exponents, the approach of plugging numbers would prove time-consuming and prone to error in this case.

9x4 – 4y4 = (3x2)2 – (2y2)2 = (3x2 + 2y2)(3x2 – 2y2).

(3x2 + 2y2)(3x2 – 2y2) = (3x2 + 2y2)

I'm not getting how (3x2 + 2y2)(3x2 – 2y2) = (3x2 + 2y2). Can someone please explain?

9x^4-4y^4=3x^2+2y^2 --> (3x^2)^2-(2y^2)^2=3x^2+2y^2 --> apply a^2-b^2=(a-b)(a+b): (3x^2-2y^2)(3x^2+2y^2)=3x^2+2y^2 --> reduce by 3x^2+2y^2: 3x^2-2y^2=1 --> x^2=\frac{2y^2+1}{3}.

Hope it's clear.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.
_________________
Manager
Joined: 07 Feb 2011
Posts: 88
Followers: 0

Kudos [?]: 4 [0], given: 43

Re: If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2 [#permalink]  25 May 2012, 16:32
Not clear still
I break down the 9x^4 expression using a difference of squares to (3x^2 -2y^2)(3x^2+2y^2) I don't get it from there on especially how the later statment equals 3x^2+2y^2 all by itself
_________________

GMAT Club team member
Joined: 02 Sep 2009
Posts: 11532
Followers: 1795

Kudos [?]: 9552 [0], given: 826

Re: If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2 [#permalink]  25 May 2012, 16:37
manimgoindowndown wrote:
Not clear still
I break down the 9x^4 expression using a difference of squares to (3x^2 -2y^2)(3x^2+2y^2) I don't get it from there on especially how the later statment equals 3x^2+2y^2 all by itself

From (3x^2-2y^2)(3x^2+2y^2)=3x^2+2y^2 divide both parts of the equation by 3x^2+2y^2 to get 3x^2-2y^2=1 --> 3x^2=2y^2+1--> x^2=\frac{2y^2+1}{3}.
_________________
Manager
Joined: 07 Feb 2011
Posts: 88
Followers: 0

Kudos [?]: 4 [0], given: 43

Re: If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2 [#permalink]  26 May 2012, 13:33
Ok let's try this one more time since I dont' think you understood which part I didn't get

how do you get from/how does (3x^2-2y^2)(2x^2+2y^2) to/equal 3x^2+2y^2
_________________

Intern
Joined: 22 Jan 2012
Posts: 35
Followers: 0

Kudos [?]: 6 [0], given: 0

Re: If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2 [#permalink]  26 May 2012, 14:13
(3x^2-2y^2)(3x^2+2y^2)=3x^2+2y^2

(3x^2-2y^2)(3x^2+2y^2) - [3x^2+2y^2 ]=0

[3x^2+2y^2 ] [(3x^2-2y^2) - (1) ] = 0
so , either [3x^2+2y^2 ] =0 or [(3x^2-2y^2) - (1) ]=0

[3x^2+2y^2 ] =0 can never be zero as question stem says that x,y are non-zero integers , so 3x^2+2y^2 will always be greater than zero .

[(3x^2-2y^2) - (1) ]=0
3x^2= 2y^2 + 1

x^2= (2y^2 + 1)/3

Hope, it is clear now
Re: If x and y are non-zero integers, and 9x^4 – 4y^4 = 3x^2 + 2   [#permalink] 26 May 2012, 14:13
Similar topics Replies Last post
Similar
Topics:
If x is an integer and y=3x+2 , which of the following 1 29 Sep 2003, 19:41
If x is an integer and y=3x+2 , which of the following 2 27 Nov 2003, 18:54
If x is an integer and y= 3x+2, which of the following 3 14 Oct 2005, 14:04
If x is an integer and y = 3x + 2, which of the ff. CANNOT 5 23 Jul 2007, 10:37
If x and y are non-zero integers, and 9x^4 - 4y^4 = 3x^2 + 4 10 Sep 2007, 18:23
Display posts from previous: Sort by