Question

If the sum of square of two positive consecutive even numbers is $100$. Then find the numbers.

Answer 1

Let the numbers be $x,x+2$ with $x>0$.

Then according to the problem,

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

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

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

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

or, $x=6$ [ Since $x>0$].

So the numbers are $6,8$.