Re: Three rational triples

HenHanna <HenHanna@dev.null> wrote:

Keith F. Lynch wrote:

Since it's been more than a week, and nobody has figured it out:
Each of them has a sum that's equal to its product and is an integer.

i think one person said exactly that.

Who and when?  I didn't see any such post.

Is it easy to find them?

No, even though there are infinitely many.  Try and find one I
didn't list.

Constraints:  All three numbers must be positive, real, and rational,
but not integers.

And of course have to be in simplest form, i.e. 1/2, not 2/4.  One
person posted "52/39, 7/6, 9/2" which is of course the same three
numbers as my "9/2, 4/3, 7/6".  And he didn't say what property
they had, anyway.

Without any constraints, x,i,-i is always a solution for any x,
if i is the square root of minus one.

How about 2 numbers

Too simple to be interesting.  If you want two numbers to have a sum
of S and a product of P, whether or not S=P, the two numbers will be
S + sqrt(S^2 - 4P) and S - sqrt(S^2 - 4P).
--
Keith F. Lynch - http://keithlynch.net/
Please see http://keithlynch.net/email.html before emailing me.