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Square roots problem

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Square roots problem

by Brent@GMATPrepNow » Wed Jan 28, 2009 8:38 am
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Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.
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by dmateer25 » Wed Jan 28, 2009 8:53 am
I multiplied both p and q by their respective conjugates to come up with

p= (sqrt(14) + sqrt(13))

q= (sqrt(14) - sqrt(13))

3pq = 3(14-13) = 3


now we have:

(sqrt(14) + sqrt(13))^2 + 3 + (sqrt(14) - sqrt(13))
27 + 2sqrt(14x13) + 3 + 27 - 2sqrt(14x13)

27 + 3 + 27
57

Fixed my silly mistake
Last edited by dmateer25 on Wed Jan 28, 2009 9:28 am, edited 1 time in total.
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by sacx » Wed Jan 28, 2009 8:55 am
p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq

= (p+q)^2 + pq

substituting values give B as answer
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by Brent@GMATPrepNow » Wed Jan 28, 2009 9:19 am
sacx wrote:p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq

= (p+q)^2 + pq

substituting values give B as answer
Nice, the answer is B.
I posted this question to note that it is sometimes beneficial to know how to simplify rational expressions involving roots. In this question, I think it speeds up the process. See what you think.

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by DeepakR » Wed Jan 28, 2009 8:01 pm
Hi Brent,

The question image isn't showing up for me. I tried it in Firefox and IE. Can someone help ? It may be an isolated case for me. :roll:
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by Brent@GMATPrepNow » Wed Jan 28, 2009 8:34 pm
DeepakR wrote:Hi Brent,

The question image isn't showing up for me. I tried it in Firefox and IE. Can someone help ? It may be an isolated case for me. :roll:
Hey DeepakR,
This is a jpeg, just like all of my other posts.
I'm not sure what to suggest.
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by DeepakR » Thu Jan 29, 2009 7:14 am
Hi Brent,

Now i am able to view the image and i get 57. Not sure what was the issue previously anyway Thanks.

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by aroon7 » Thu Jan 29, 2009 9:07 pm
Brent Hanneson wrote:
Nice, the answer is B.
I posted this question to note that it is sometimes beneficial to know how to simplify rational expressions involving roots. In this question, I think it speeds up the process. See what you think.

Image
Thanks Bernt
I get reminded about conjugates that i learnt in school...
may be it helps me at the test
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