Ta có: $x + y = 15$
$\Rightarrow (x + y)^{2} = 15^{2} = 225$
$\Rightarrow x^{2} + y^{2} = 225 - 2xy $
$\Rightarrow x^{2} - 2xy + y^{2} = 225 - 4xy$
$\Rightarrow (x - y)^{2} = 225 - 4.56 = 1$
$\Rightarrow x - y = 1$
$N = x^{2} - y^{2} = (x + y)(x - y) = 15.1 = 15$