# Math Help - How should I solve this question?

1. ## How should I solve this question?

Write the reciprocal of 2 + 5sqrt(3) in the form of a + bsqrt(3).

Thanks !

2. Originally Posted by beta12
Write the reciprocal of 2 + 5sqrt(3) in the form of a + bsqrt(3).

Thanks !
The reciprocal is,
1/(2+5sqrt(3))
Multiply numerator and denominator by 2-5sqrt(3) thus,
(2-5sqrt(3))/(4-25*3)=(2/71)+(-5/71)sqrt(3)
So,

a=2/71
b=-5/71

But this not really a number theory question.

3. Hi perfecthacker,

Thanks.

No, this question is from my number theory book. I thought solving it involving number theory technique.

4. Originally Posted by beta12
No, this question is from my number theory book. I thought solving it involving number theory technique.
Based on your previous question I assume you are learning how to express quadradic numbers in a periodical continued fraction form. In order to do that it help to rationalize the denomiator of these numbers.

5. Hi Perfecthacker,

Yes. You are right.

Thanks.