Question

if n,m belongs to N and m = ( n^2 - n - 35)/( n - 4), then find the value of m.

Answer 1

I hope this answer help you

Answer 2

First of all we have to resolve this term m = (n² - n - 35)/(n - 4).
arrange the numerator in such a way that it contains (n -4)

Now, n² - n - 35 = n² - 4n + 3n - 12 - 23
= n(n -4) + 3(n -4) - 23
= (n + 3)(n -4) -23

Hence, m = {(n +3)(n -4) - 23}/(n -4)
m = (n +3)(n-4)/(n-4) - 23/(n -4)
m = n +3 - 23/(n -4)
∵ m and n both are natural number ∴ 23/(n -4) should be natural number
it is possible when (n -4) = 23 ⇒n = 27
∴ m = 27 + 3 - 23/23 = 29

Hence, m = 29 and n = 27