[tex]x^2+y^2=(x^2+2xy+y^2)-2xy \\ \\ x^2+y^2=(x+y)^2-2xy \\ \\ 2xy=(x+y)^2-(x^2+y^2)=(2a\sqrt{5})^2-48a^2=20a^2-48a^2=-28a^2. \\ \\ \\ \\ x^2+y^2=(x^2-2xy+y^2)+2xy \\ \\ x^2+y^2=(x-y)^2+2xy \\ \\ (x-y)^2=x^2+y^2-2xy=48a^2-(-28a^2)=76a^2 \\ \\ x-y=\pm \sqrt{76a^2}=\pm 2\sqrt{19}a[/tex]
