Hi,
I have the final result of this below problem (which is n=2, 5) but i can´t seem to find how to pass the limitation part.
Find all the n, in IN in which 2n^2+ 1 | n^3 + 9n - 17:
So i used the system and reduced the n^3
2n^2+ 1 | n^3 + 9n - 17
2n^2 + 1 | 2n^2 + 1
(=) 2n^2 + 1 | (n^3 + 9n - 17) (2) + (2n^2 + 1)(-n)
(=) 2n^2 + 1 | 17n - 34
(=) 17n-34=0 V 2n^2+1 <= 17n-34
(=) n=2 V |2n^2+1| <= |17n-34|
From here i know the n=2. so i only need to work the below:
|2n^2+1| <= |17n-34|
(=) 2n^2+1 <= 17n+34
I think the steps i did above are correct, but i can´t seem to pass here. In the book, says this expression will result in n=1,4,5, but i tried solving it with like an inequation and i don´t get those results.
If anyone could help i would apreciate.
I have the final result of this below problem (which is n=2, 5) but i can´t seem to find how to pass the limitation part.
Find all the n, in IN in which 2n^2+ 1 | n^3 + 9n - 17:
So i used the system and reduced the n^3
2n^2+ 1 | n^3 + 9n - 17
2n^2 + 1 | 2n^2 + 1
(=) 2n^2 + 1 | (n^3 + 9n - 17) (2) + (2n^2 + 1)(-n)
(=) 2n^2 + 1 | 17n - 34
(=) 17n-34=0 V 2n^2+1 <= 17n-34
(=) n=2 V |2n^2+1| <= |17n-34|
From here i know the n=2. so i only need to work the below:
|2n^2+1| <= |17n-34|
(=) 2n^2+1 <= 17n+34
I think the steps i did above are correct, but i can´t seem to pass here. In the book, says this expression will result in n=1,4,5, but i tried solving it with like an inequation and i don´t get those results.
If anyone could help i would apreciate.
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