The sum of two numbers is $6$ times their geometric mean.Show that the ratio of the numbers is $3+2\sqrt 2\::\:3-2\sqrt 2$

Question

$\begin{array}{1 1}3+2\sqrt 2: 3-2\sqrt 2 \\ 4+2\sqrt 2: 2-2\sqrt 2 \\3+3\sqrt 2: 3-3\sqrt 2 \\ 3+2\sqrt 3: 3-2\sqrt 3\end{array}$