2 and 3, what could be worse?

Take two numbers that add to 2 and multiply to 3. What is the sum of the reciprocals of these two numbers?

The “truly mind-blowing” way to do this is like how I did it, going through the quadratic formula and such.

Let a be one of the numbers, therefore the other number is 2-a. a(2-a) = 3, -a^2 + 2a – 3 = 0, and a becomes 1±i√2. Adding the reciprocals… that’s when the easier answer comes up.

I couldn’t believe that I couldn’t see this.

You know how 1/a + 1/b = (a+b)/ab? That means, whatever the values of a and b are, the sum of the reciprocals are 2/3.

Why couldn’t I see this when I first solved it…

I’m not taking any credit for this puzzle, I read it in Mathematical Curiosities by Alfred S. Posamentier and Ingmar Lehmann. It’s a great book, I suggest you read it if you can.

All for today, and I’m considering posting more carefully and uploading every week or so.

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