I was wondering if someone could show me the way to write this one up.
The sum of a number and it's reciprocal is 2 1/6 . What is the number? (sounds like fraction)
I got this far......
x+y= 2 1/6
x= 2 1/6-y
y= 2 1/6-x
Where do I go from here to find the answer?
Hi there....you know I was wondering if you could show or explain the treatment I need to do to xy=6 (as it's multiplied) so that I can use it as substitution in x2+y2=13.
It's probably simple, but I don't know. I understand the above fraction work in getting the common denominator.
Thankyou.
Simplest is...we are looking for integers x and y, so you can just factor the 6 into 3(2).
Or 13=1+12, 2+11, 3+10, 4+9....4 and 9 are squares.
You could do it purely in algebra with
Now substitute this into the other to get x only..
Multiply both sides by
Both are equal, subtract to get zero, then factor
then
etc
Thanks Archi,
I could follow your second example better. So x=3, or x=2. Is there a process for turning that into a fraction of 3/2 0r 2/3, or do we just use logic, to explain that it is their sum that equals to 2 1/6, so therefore that is it? I liked the logic of explaining the integers! With the first example I don't see how you got 3 lots of (a+b) in the numerator...(a+b)(a+b)b(a+b)over b(a+b). I thought it would have been (a+b)(a+b)b2 over b(a+b). Don't you multilpy the numerator and denominator, by the other fractions denominator to balance the fractions? I understand the rest of the example after that. But in the first place, how did you come up with (a+b)/b and b/(a+b). I understand the use of a/b and b/a. Pardon my ignorance, and thanks for your time.
Tren301
Hi Tren301,
The way I did it in the first post is the same as that.
I used as one of the numbers is bigger than 1, since
in other words, one of the numbers cannot be 1, so one is bigger than 1 and the other is smaller than 1.
Those two fractions now have a common denominator, so the numerators can be combined.
There was a typo in that earlier post... now fixed.