Original post by kit2247
I don’t understand why can’t the consecutive odd integers be (2n+1)^2 and (2n+3)^2 . I’ve used these but my answer doesn’t show it’s two more than a multiple of 8
I get an answer of 8(n^2+2n) +10
I get an answer of 8(n^2+2n) +10
10 = 8 + …
Also, you can use 2n + 1 and 2n + 3, as they would be consecutive odd numbers.
(edited 10 months ago)
Original post by TypicalNerd
10 = 8 + …
I’m so confused
Original post by kit2247
I’m so confused
Ok, 10 = 8 + whatever
Now replace the 10 with the 8 + whatever and see how that changes your answer
Original post by TypicalNerd
Ok, 10 = 8 + whatever
Now replace the 10 with the 8 + whatever and see how that changes your answer
Now replace the 10 with the 8 + whatever and see how that changes your answer
That doesn’t seem to get the answer they are looking for
Original post by kit2247
That doesn’t seem to get the answer they are looking for
It will. 8 also has a factor of 8, so can you fit it into the factored part?
Edit: bear in mind you’ve used different odd integers to the MS, so your expression will differ slightly from the MS, but it’ll still be possible to reach the same conclusion as the MS wants you to
(edited 10 months ago)
Original post by TypicalNerd
It will. 8 also has a factor of 8, so can you fit it into the factored part?
Edit: bear in mind you’ve used different odd integers to the MS, so your expression will differ slightly from the MS, but it’ll still be possible to reach the same conclusion as the MS wants you to
Edit: bear in mind you’ve used different odd integers to the MS, so your expression will differ slightly from the MS, but it’ll still be possible to reach the same conclusion as the MS wants you to
but why did you include an equals? I’m not sure why you are assuming that 10=…?
Original post by kit2247
but why did you include an equals? I’m not sure why you are assuming that 10=…?
I hope we can both agree that 10 = 8 + 2 (which is what I was hoping you’d notice but perhaps I wasn’t choosing the best way to point it out).
The point of the question is to show that the result is always 2 more than a multiple of 8, so we have to extract a 2 from somewhere. The only way you can do that is getting it from the constant term, + 10.
Its also worth noting that representing consective odd integers as (2n-1) and (2n+1) will give a simpler final expression as the odd power terms will cancel and only even power terms will be left in
(2n-1)^2 + (2n+1)^2
so the answer 8n^2+2 only contains even powers so its easier to prove the property theyre after. As above, choosing (2n+1) and (2n+3) will give a different but equivalent answer n <-> n+1, as
8(n+1)^2 + 2 = 8(n*2+2n+1) + 2 = 8(n^2+2n) + 10
So there is just a shift in n by 1 between your answer and their answer, so youve chosen to use the next set of consecutive odd numbers.
(2n-1)^2 + (2n+1)^2
so the answer 8n^2+2 only contains even powers so its easier to prove the property theyre after. As above, choosing (2n+1) and (2n+3) will give a different but equivalent answer n <-> n+1, as
8(n+1)^2 + 2 = 8(n*2+2n+1) + 2 = 8(n^2+2n) + 10
So there is just a shift in n by 1 between your answer and their answer, so youve chosen to use the next set of consecutive odd numbers.
(edited 10 months ago)
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