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Question about conjugates

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Question about conjugates

by EMAN » Sat Sep 19, 2009 10:49 am
Okay, so if I have 1 / (SQRT N + 1) - (SQRT N), then I want to take the conjugate, you only have to change the sign in the middle I would assume, correct? For instance, the conjugate would be (SQRT N + 1) PLUS(+) (SQRT N), not (SQRT N - 1) + (SQRT 1).
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Re: Question about conjugates

by Brent@GMATPrepNow » Sun Sep 20, 2009 10:50 am
EMAN wrote:Okay, so if I have 1 / (SQRT N + 1) - (SQRT N), then I want to take the conjugate, you only have to change the sign in the middle I would assume, correct? For instance, the conjugate would be (SQRT N + 1) PLUS(+) (SQRT N), not (SQRT N - 1) + (SQRT 1).
Yes, you're right.
In general, the conjugate of A+rootB is A-rootB and vice versa.

For others seeing the word "conjugate" for the first time, we use often conjugates to rewrite rational expressions (fractions) in order to remove the roots from the denominator.

So, to find a fraction equivalent to the fraction (root3 + root4)/(root7 - root 4) we would multiply both numerator and denominator by (root7 + root4). Doing so, will give us a new denominator of 3.

Try it out.
Brent Hanneson - Creator of GMATPrepNow.com
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