G.M. = 4, H.M. = (\dfrac{16}{5})

[ \sqrt{xy}=4\implies xy=16 ] [ \dfrac{2xy}{x+y}=\dfrac{16}{5}\implies\dfrac{32}{x+y}=\dfrac{16}{5}\implies x+y=10 ]

[ t^2-10t+16=0\implies(t-8)(t-2)=0 ]

Answer: 2 and 8