Question

The product of two consecutive natural numbers is $72$. Find the numbers.

Answer 1

Let the two consecutive natural numbers be $x$ and $(x+1)$
From the given condition, we have
$x(x+1)=72$
$\Rightarrow x^2+x=72$
$\Rightarrow x^2+x-72=0$
$\Rightarrow x^2+9x-8x-72=0$
$\Rightarrow x(x+9)-8(x+9)=0$
$\Rightarrow (x-8)(x+9)=0$
$\Rightarrow x-8=0$ or $x+9=0$
$\Rightarrow x=8$ or $x=-9$
$\because -9$ is not a natural number.

So, $x=8$ and $x+1=8+1=9$.
Hence, the numbers are $8$ and $9$.