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Updated on: 23 Jan 2022, 03:11
Originally posted by manimgoindown on 25 May 2012, 15:14.
Last edited by Bunuel on 23 Jan 2022, 03:11, edited 2 times in total.
Last edited by Bunuel on 23 Jan 2022, 03:11, edited 2 times in total.
Edited the question and moved to PS subforum
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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?
A. \(\frac{4y^2}{3}\)
B. \(2y^2\)
C. \(\frac{(2y^2+1)}{3}\)
D. \(2y^2\)
E. \(\frac{6y^2}{3}\)
A. \(\frac{4y^2}{3}\)
B. \(2y^2\)
C. \(\frac{(2y^2+1)}{3}\)
D. \(2y^2\)
E. \(\frac{6y^2}{3}\)
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?
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?
25 May 2012, 15:32
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manimgoindowndown
Welcome to GMAT Club. Below is an answer to your question.
\(9x^4-4y^4=3x^2+2y^2\);
\((3x^2)^2-(2y^2)^2=3x^2+2y^2\);
Apply \(a^2-b^2=(a-b)(a+b)\) to get \((3x^2-2y^2)(3x^2+2y^2)=3x^2+2y^2\);
Reduce by \(3x^2+2y^2\) to get \(3x^2-2y^2=1\);
\(x^2=\frac{2y^2+1}{3}\).
Answer: C.
Hope it's clear.
General Discussion
25 May 2012, 16:32
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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
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
