Surds Problem

[kalyan601]

Hi, when I first looked at this question, I thought I should be able to solve it easily, but I realised that I didn't know how to solve it.
Can someone tell me if I've done it right?

Express (2(3+√5))/(3-√5) in the form b + c √5 where b and c are integers.

(2(3+√5))/(3-√5) = (2(3+√5)(3+√5))/((3-√5)(3+√5))
= (9+6√5+5)/(9-5)
=(12+6√5)/4
=3+(2/3)√5
b=3
c=2/3

Is this right?

Thanks

 

[Ishuda]

Pretty close but the last time I looked 9 and 5 were 14, not 12. Of course I never make misteaks

 

[wjm11]

Hi, when I first looked at this question, I thought I should be able to solve it easily, but I realised that I didn't know how to solve it.
Can someone tell me if I've done it right?

Express (2(3+√5))/(3-√5) in the form b + c √5 where b and c are integers.

(2(3+√5))/(3-√5) = (2(3+√5)(3+√5))/((3-√5)(3+√5))
= (9+6√5+5)/(9-5)
=(12+6√5)/4
=3+(2/3)√5
b=3
c=2/3

Is this right?

Thanks

Your approach is correct. There are a few errors/typos.

(2(3+√5))/(3-√5) = (2(3+√5)(3+√5))/((3-√5)(3+√5))
= (2)(9+6√5+5)/(9-5)
=(2)(14+6√5)/4
=(14+6√5)/2
= 7+3√5