Question

The product of two consecutive positive integers is $306$. We need to find the integers.

Answer 1

Let two positive integers be $n$ and $(n+1)$

$\Rightarrow n(n+1)=306$

$\Rightarrow n^2+n-306=0$

$\Rightarrow n^2+18n-17n-306=0$

$\Rightarrow n(n+18)-17(n+18)=0$

$\Rightarrow (n+18)(n-17)=0$

$\Rightarrow n+18=0$ (OR) $n-17=0$
If $n+18=0\Rightarrow n=-18$

Since, $n$ is negative. So $n=-18$ cannot be exist.

Now, lets take $n-17=0$

$\Rightarrow n=17$

$\Rightarrow n+1=18$

Therefore, required positive integers are $17$ and $18$.