Question

The product of two consecutive natural numbers is $56$. Find the numbers.

Answer 1

Let the two consecutive natural numbers be $x$ and $(x+1)$.
From the given condition,
$x(x+1)=56$
$\Rightarrow x^2+x=56$
$\Rightarrow x^2+x-56=0$
$\Rightarrow x^2+8x-7x-56=0$
$\Rightarrow x(x+8)-7(x+8)=0$
$\Rightarrow (x-7)(x+8)=0$
$\Rightarrow x-7=0$ or $x+8=0$
$\Rightarrow x=7$ or $x=-8$
$\because -8$ is not a natural number.

So, $x=7$ and $x+1=7+1=8$.
Hence, the numbers are $7$ and $8$.