Found something interesting while playing with numbers, is there a name for this?
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Guys, I was randomly playing with numbers and noticed something weird lol.
3 + 3/2 = 3 × 3/2
Both give 4.5. I got curious and started checking if there is any way to generalise this.
So I started with
a + b = ab
Then rearranged it:
ab - b = a
b(a - 1) = a
So,
b = a/(a - 1)
Then I realised I can take almost any number and find another number which satisfies this.
For example, if I take 8, then b = 8/7.
8 + 8/7 = 8 × 8/7 = 64/7
I also tried another approach. If I say both the sum and product should equal some number c, then
a + b = c
ab = c
Using the quadratic formula, I got
a, b = (c ± √(c² - 4c))/2
So if I choose c = 88, I get two numbers whose sum and product are both 88.
I know this is probably already known maths and not some new discovery haha, but I was happy that I managed to derive the formula myself.
Is there any particular name for this relationship, or anything interesting related to it? Just curious if this leads to something else.