chets wrote:
the reason i posted this question was to ask a second question.
if you chose to multiply the numerator and denominator by sqrt(5)+sqrt(3) you get 4+sqrt(5)*sqrt(3)
though, if you chose to multiply the numerator and denominator by sqrt(5)-sqrt(3) you get 1 / (4-sqrt(5)*sqrt(3))
though seemingly different,
4+sqrt(5)*sqrt(3) = 1/(4-sqrt(5)*sqrt(3))
I am not sure whether there is a broad generalization i am missing. If anyone can shed light on this, that would be great!
Chet,
You r not missing anything,
You get:
1/(4-sqrt(5)*sqrt(3)) =
(4+sqrt(5)*sqrt(3)) / [(4-sqrt(5)*sqrt(3))(4+sqrt(5)*sqrt(3))] =
(4+sqrt(5)*sqrt(3)) / (16 - 15) =
(4+sqrt(5)*sqrt(3))
Hope that helps