It may depend on how you define p and q. Do they belong to , or ?
(2√3 - 1)² = p + q√3
Does anyone know how to solve this?
So far I've only got:
13 - 4√3 = p + q√3
However, as with a similar problem I have done, I am pretty sure there are a range of answers, not just p = 13 and q = -4.
Can someone help me with this?
: set of natural integers (means the positive ones)
: set of all integers (positive and negative)
: rational numbers, which means with p and q in (and q different from 0)
: set of all numbers, including irrational ones.
is included in , which is included in , which is included in
Why did I ask ? Because if we're working on , there is only one solution.
If we're working on , then and are solutions, for example, but there is an infinity of possibilities. (note that is an irrational and only belongs to ).
So the solutions will be
So we want and
Hence a=13-3d and b=-4-c.
-------> general solutions are and , this time, c and d belonging to (yep Isomorphism, it can be done this way indeed )
This is only for the ones involving the basic way. Otherwise, there is an infinity of them.
wow. I didn't get a word of the second-last post that you posted (the one with all the equations...)
I'll be sticking with the simple solution of p = 13 and q = -4 then.
Thanks for your help
Edit: oops, yes I did mean Q. all the letters are getting to my head.