Question

The product of two consecutive positive even numbers is $168$. Find them,

Answer 1

Let two consecutive even numbers be $2x$ and $2x+2$.

According to question:

$2x(2x+2)=168$

$\Rightarrow 4x^2+4x-168=0$

$\Rightarrow x^2+x-42=0$

$\Rightarrow x^2+7x-6x-42=0$

$\Rightarrow x(x+7)-6(x+7)=0$

$\Rightarrow (x+7)(x-6)=0$

$\Rightarrow x=-7,x=6$

But $x$ cannot be negative.

$\therefore$ If $x=6$ then $2x=12$ and $2x+2=14$

$\therefore$ Two consecutive even numbers are $12$ and $14$