Question

The product of two positive consecutive integers is $462$. Find those numbers.

Answer 1

Let the integers be $x$ & $x+1$

Then,

$x(x+1)=462$

$\Rightarrow x^2+x-462=0$

$\Rightarrow x+22x-21x-462=0$

$\Rightarrow x(x+22)-21(x+22)=0$

$\Rightarrow (x+22)(x-21)=0$

So $x=21$ or $x=-22$.

But it is given that the positive integers have been taken into consideration. So, $x=-22$ is not a valid solution.

If $x=21$ then,

$x+1=21+1$

$=22$

So, $21$ and $22$ and the two consecutive positive integers whose product is equal to $462$.