Question

The product of two consecutive natural numbers is $42$. Find the numbers.

Answer 1

Let the two consecutive natural numbers be $x$ and $(x+1)$
From the given condition,we have
$x(x+1)=42$
$\Rightarrow x^2+x=42$
$\Rightarrow x^2+x-42=0$
$\Rightarrow x^2+7x-6x-42=0$
$\Rightarrow x(x+7)-6(x+7)=0$
$\Rightarrow (x-6)(x+7)=0$
$\Rightarrow x-6=0$ or $x+7=0$
$\Rightarrow x=6$ or $x=-7$ .....[Since $-7$ is not a natural number]

So, $x=6$ and $x+1=6+1=7$.
Hence, the numbers are $6$ and $7$.