I am just looking through my course notes right now.
I notice the prof went to multiply two terms and I am kind of lost on the method he used here.
A problem here is that I don't know how to show root of with my keyboard LOL. I am sure someone will
(a+b√2)(c+d√2)=(ac+2bd)+(ad+bc)√2
Is this correct or did I copy something down wrong?
Ok there were two reasons why this confused me.
1. the 2bd which should be clear to me.....ooops
2.In my notes where there should have been a "c" where there was an "a" so I was getting a^2 haha ...math in the morning.
But now I have another similar related question about some simple algebra
I have
(a-b√2)/(a^2-2b^2) =( a/a-2b^2)-(b/a^2+2b^2) where did the √2 go?
EDIT: For this one I should have added context. Because from a similar proof it removes the √2 because a and b are rational. I still dont get the nest part though...
From that he went to a^2-2b^2 Not sure what happened here.
You can see it in contest in this link.
Look under the heading "Inverses"
Numbers of Type Rational a plus b root 2 Form a Field - ProofWiki
I don't see this equation in the link you provided. The link says that the inverse of , which is , equals , with in the nominator of the second term. The coefficients and are rational number when and are.
By the way, according to the standard arithmetic operation precedence, a/a-2b^2 means (a/a)-2b^2 = 1 - 2b^2. It should probably be a/(a^2-2b^2).