Question

The sum of the square of two consecutive positive even integers is $100$ then find the integers.

Answer 1

Let the two consecutive positive even numbers be x and $(x+2)$

According to the problem,

$x^2+(x+2{)}^2=100$

or, $2x^2+4x+4=100$

or, $x^2+2x-48=0$

or, $(x+8)(x-6)=0$

$\because x>0$ this gives, $x=6$

So, the numbers are $6$ & $(6+2)=8$.