Question

Sum of the squares of two consecutive positive even integers is $100$; find those numbers by using quadratic equations.

Answer 1

Let $x$ and $(x+2)$ be the consecutive even integers. We get
$x^2+(x+2{)}^2=100$
expanding, we get
$x^2+x^2+4x+4=100$
setting = $0$, we get
$2x^2+4x-96=0$
Dividing by $2$ , we get,
$x^2+2x-48=0$
factoring, we get,
$(x+8)(x-6)=0$
solving for x, we get
$x+8=0$ = $x=-8$
and $x-6=0=x=6$.
so, we have
$(-8,-6)$ OR $(6,8)$