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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
Last visit: 02 Mar 2015
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Concentration: General Management, Nonprofit
Schools: HBS '17 (M) Stanford '17 (A)
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.
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