Question

If n, $m\in N$ and $m=\frac{n^2-n-35}{n-4}$ , then find the value of m

Answer 1

$m=\frac{n^2-n-35}{n-4}⟹n^2-n-35$ must be divisible by $n-4$ which is not possible so only case is $n-4=-1,n^2-n-35<0$ or $n-4=1,n^2-n-35>0$

$⟹n=3,5$

$(3{)}^2-3-35<0,(5{)}^2-5-35<0$

So $n=3⟹m=\frac{3^2-3-35}{3-4}=29$