Fractional puzzle
After seeing a blog post here talking about a puzzle tweeted by Colin Beveridge, I thought I’d have a go.
The puzzle is:
xy = 3
x + y = 2
What is the value of 1/x + 1/y ?
Despite @srcav’s beliefs, I do like a good pure maths problem (we just seem to disagree about what counts as good). So I broke out my felt tip pens and here is my working:
If you’ve read the link you’ll know that the quadratic approach leads you into complex numbers. Now, while I can do those, I thought I’d try another approach before going down that route:
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It’s quite satisfying that it comes out so nicely. The part in square brackets turned out to be a route I didn’t want to pursue but I quite like leaving my abandoned routes in my working.
So, thanks Colin, that was fairly interesting to have a play with. Thanks to Cav for highlighting it too.
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reflectivemaths's Blog 
Am I missing something here?
Doesn’t 1/x + 1/y = (y+x)/(xy) = 2/3 by using algebraic fractions?
Hi.
Yes you’re right. That’s another way of doing it.
Dave
All the above working is mere wasting of time and space!!. Just divide the second equation by the first equation. Thats it. You get the answer!!!!
That does work but I still like my way too. 🙂