Square roots problem

[Brent@GMATPrepNow]

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.

[dmateer25]

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

[sacx]

p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq

= (p+q)^2 + pq

substituting values give B as answer

[Brent@GMATPrepNow]

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.

[DeepakR]

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:

[Brent@GMATPrepNow]

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.
Brent

[DeepakR]

Hi Brent,

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

- Deepak

[aroon7]

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.

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