If m and n are integers and m = n - (2/n) - (2/n^2), then which of the following could be the value of m?
i. -5
ii. -3
iii. -1
(A) ii only
(B) ii and iii only
(C) i and ii only
(D) i and iii only
(E) i, ii, and iii
i know the answer is B but i have no idea how to get it without using guess and check, which takes forever
i. -5
ii. -3
iii. -1
(A) ii only
(B) ii and iii only
(C) i and ii only
(D) i and iii only
(E) i, ii, and iii
i know the answer is B but i have no idea how to get it without using guess and check, which takes forever
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n^2 has to be less than or equal to 2 for the function to yield an integer (2/n^2 has to be an integer). anything else leads to a fractional value for m. division by 0 is undefined, so that leaves only 1 and -1 as possible values for n. plug those in and you get -3.
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m = n - (2/n) - (2/n^2)
Consider the value of 'n' as a positive integer +1,we get,
m = 1 - (2/1) - (2/1^2)
m = 1 - 2 - 2
Therefore, m = -3.
Again,consider the value of 'n' as a negative integer -1,we get,
m = -1 - (2/-1) - ((2/(-1)^2)
m = -1 + 2 - 2
Therefore, m = -1.
So, the answer is (B).
Consider the value of 'n' as a positive integer +1,we get,
m = 1 - (2/1) - (2/1^2)
m = 1 - 2 - 2
Therefore, m = -3.
Again,consider the value of 'n' as a negative integer -1,we get,
m = -1 - (2/-1) - ((2/(-1)^2)
m = -1 + 2 - 2
Therefore, m = -1.
So, the answer is (B).