Question

The product of two consecutive positive integers is $306.$ Find the two integers$?$

Answer 1

Let us assume

The first integer number $=x$

Thus$,$ the next consecutive positive integer will be$=x+1$

Product of two consecutive integers $=x\times \left(x+1\right)$

$x\times \left(x+1\right)=306$

$x^2+x=306$

$x^2+x-306=0.....\left(1\right)$

$x^2+18x-17x-306=0$

$x\left(x+18\right)-17\left(x+18\right)=0$

$\left(x+18\right)\left(x-17\right)=0$

$x+18=0$ or $x-17=0$

$x=-18$ or $x=17$

Since integers are positive

so $17$ and $18$ are two positive integers.

Hence, two consecutive positive integers are $17$ and $18$.