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Fri Feb 09, 2024 11:25 am
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D
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Difficulty:
15%
(low)
Question Stats:
87% (02:09) correct
13%
(02:38)
wrong
based on 631
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Date
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What is the value of \(\frac{x^6y^2 - x^2y^6}{x^2 + y^2}\) if \(x = \frac{3}{2}\) and \(y = \frac{1}{2}\)?
A. 6
B. \(5\frac{1}{8}\)
C. 5
D. \(1\frac{1}{8}\)
E. 0
A. 6
B. \(5\frac{1}{8}\)
C. 5
D. \(1\frac{1}{8}\)
E. 0
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Fri Feb 09, 2024 11:26 am
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Bunuel
- \(\frac{x^6y^2 - x^2y^6}{x^2 + y^2} = \)
\(=\frac{(xy)^2(x^4 - y^4)}{x^2 + y^2} = \)
\(=\frac{(xy)^2(x^2 - y^2)(x^2 + y^2)}{x^2 + y^2} = \)
\(=(xy)^2(x^2 - y^2)= \)
\(=(\frac{3}{2}*\frac{1}{2})^2((\frac{3}{2})^2 - (\frac{1}{2})^2) = \)
\(=(\frac{9}{16})(2) = \)
\(=\frac{9}{8}=\)
\(=1\frac{1}{8}=\)
Answer: D.
General Discussion
Sat Mar 09, 2024 9:24 am
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Hey Bunuel -- I'm curious if you could describe or write out that first step of simplification?
I went a different route but it felt messy, and your path seems simpler but I'm a bit conufsed how you factored out (xy)^2 from both sides of the numerator... thank you
I went a different route but it felt messy, and your path seems simpler but I'm a bit conufsed how you factored out (xy)^2 from both sides of the numerator... thank you
