Question

The product of two consecutive natural numbers is $30$. Find the numbers.

Answer 1

Let the two consecutive natural numbers be $x$ and $(x+1)$
From the given condition, we have
$x(x+1)=30$
$\Rightarrow x^2+x=30$
$\Rightarrow x^2+x-30=0$
$\Rightarrow x^2+6x-5x-30=0$
$\Rightarrow x(x+6)-5(x+6)=0$
$\Rightarrow (x-5)(x+6)=0$
$\Rightarrow x-5=0$ or $x+6=0$
$\Rightarrow x=5$ or $x=-6$
Since, $-6$ is not a natural number.

So, $x=5$ and $x+1=5+1=6$.
Hence, the numbers are $5$ and $6$.