x=2-\sqrt{5}
y=2+ \sqrt{5}
x*y=(2-\sqrt{5})(2+\sqrt{5})=2^2-\sqrt{5}^2=4-5=-1
\frac{x}{y}=\frac{2-\sqrt{5}}{2+ \sqrt{5} }=\frac{( 2-\sqrt{5} )(2-\sqrt{5})}{(2+ \sqrt{5})(2-\sqrt{5})}=\frac{(2-\sqrt{5})^2}{2^2+ \sqrt{5}^2}=\frac{2^2-2*2\sqrt{5}-\sqrt{5}^2}{4+5}=
\frac{4-4\sqrt{5}-5}{9}=\frac{-4\sqrt{5}-1}{9}
x^2+y^2=(2-\sqrt{5})^2+(2+ \sqrt{5} )^2=4-2 \sqrt{5} +5+4+2 \sqrt{5} +5=8+10=18