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27 Jun 2010, 16:42
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On the iphone app the following equation was simplified
M+N- 2 Sqrt(MN)
to
(sqrt(m)-sqrt (N))^2
This simplification was not immediately apparent to me. What did I not see. What should have I been looking for
M+N- 2 Sqrt(MN)
to
(sqrt(m)-sqrt (N))^2
This simplification was not immediately apparent to me. What did I not see. What should have I been looking for
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whiplash2411
Joined: 09 Jun 2010
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27 Jun 2010, 16:56
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Whenever you look at something of the form: \(a^2 + b^2 + 2*a*b\) or \(a^2 + b^2 - 2*a*b\), just simplify to \((a+b)^2\) or \((a-b)^2\)
27 Jun 2010, 17:14
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Jinglander
Great question!
The ability to recognize certain patterns will save you a lot of time on Test Day. Two of the most commonly recurring patterns on the GMAT are special quadratic expressions.
The more common of the two is a difference of squares:
a^2 - b^2 = (a + b)(a - b)
The less common of the two is a perfect square, which can appear in two forms:
(a + b)^2 = a^2 + 2ab + b^2
and
(a - b)^2 = a^2 - 2ab + b^2.
Now what the GMAT loves to do is test us on conventional rules in unconventional ways. So, if the problem you were looking at had read:
m^2 - 2mn + n^2
it would have been easy to recognize it as a perfect square. What your question has done is take this common form and make it look weirder:
m - 2(sqrt(mn)) + n
which follows the exact same pattern.
So, since m^2 - 2mn + n^2 = (m - n)^2
and since m - 2(sqrt(mn)) + n is the exact same pattern, it simplifies to:
(sqrt(m) - sqrt(n))^2
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
