Question

The square of the greater of two consecutive even numbers exceeds the square of the smaller by $37$. Find the numbers.

Answer 1

let the numbers be $x,x+1$

Their squares are $x^2,(x+1{)}^2$

The difference is $37$

$⟹(x+1{)}^2-x^2=37x^2+2x+1-x^2=372x+1=372x=36x=18$

So the numbers are $18,19$