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by gmatblood » Mon Nov 07, 2011 9:43 pm
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 x^2 in terms of y?

-4(y^2)/3


-2y^2


(2[y^2]+1)/3


2y^2


[6y]^2/3
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by shankar.ashwin » Mon Nov 07, 2011 9:49 pm
Let X = x^2 and Y = y^2

So we have 9X^2 - 4Y^2 = 3X+2Y
(3X+2Y) * ( 3X- 2Y) = 3X+2Y

3X-2Y = 1

3X =1+ 2Y
X =(1+ 2Y)/3 (or)
x^2 =(1+ 2y^2)/3
C IMO
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by Anurag@Gurome » Mon Nov 07, 2011 10:00 pm
gmatblood 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 x^2 in terms of y?
Note that for x = y = 1, the given relation holds.
Hence, the correct option is the one which is equal to x^2 = 1 for y = 1.
  • A. -4(y^2)/3 = -4/3 ----> NO
    B. -2y^2 = -2 ----> NO
    C. (2[y^2]+1)/3 ----> (2 + 1)/3 = 1 ----> YES
    D. 2y^2 = 2 ----> NO
    E. [6y]^2/3 = (6^2)/3 = 12 ----> NO
The correct answer is C.
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