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leios
3 consecutive numbers, add and multiply to get the same result
About the author
Hello I'm an 12th grade student
Quick Summary
The idea is let's say three consecutive numbers x,x+1,x+2. And we solve x(x+1)(x+2)=x+x+1x+2 Since it is difficult to solve, we solve by taking, x-1,x,x+1. And then we expand it to 2,4,5... Consecutive numbers. Then we space the numbers by 2,3,4... And then we include real and complex numbers
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I am looking for a manimator
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contact: Discord, JRBros#4538
Additional context
Side note: this idea probably won't get a prize. I you wish for a prize, then please select other topic. This is a topic I think is fun
I'm confused.
Did you mean try to solve x (x + 1) (x + 2) = x + (x + 1) + (x + 2) ?
If so that is equivalent to x^3 + 3*x^2 - x - 3 = (x - 1) * (x + 1) * (x + 3) = 0, and thus there are 3 solutions {-3,-1,1}
Hi! as @edgarcosta mentions it has 3 solutions, because:
1+2+3=1*2*3
-1-2-3=-1*-2*-3
-1+0+1=-1*0*1
This is an equation of the form abc = a+b+c where a,b and c are consecutive. This formula appears in a Mathologer video you might want to check it out, maybe its useful 👍
https://www.youtube.com/watch?v=IguNXoCjBEk
I mean also solve 4 numbers, 5 numbers upto n numbers, like a general formula or pattern. And increase the increment from 1 to m