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by gmat212 » Wed Jan 07, 2009 1:21 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 x2 in terms of y?


A: (2y2+1)/3



I understand the diff of 2 sq's so
9x^4 – 4y^4 =

(3x^2+2y^2) (3x^2-2y^2)= (3x^2-2y^2)

then what?


Thanks
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by DavoodBeater » Wed Jan 07, 2009 2:09 pm
9x^4 – 4y^4 = (3x^2+2y^2) (3x^2-2y^2)
and
9x^4 – 4y^4 = 3x^2+2y^2
then:

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