[tex](2 \sqrt{2} - 1 {)}^{2} + (2 \sqrt{2} + 1 {)}^{2} = {x}^{2} \\ 8 - 4 \sqrt{2} + 1 + 8 + 4 \sqrt{2} + 1 = {x}^{2} \\ 9 - 4 \sqrt{2} + 9 + 4 \sqrt{2} = {x}^{2} \\ {x}^{2} = 18 \\ x = \sqrt{18} \\ x = \sqrt{9 \times 2} \\ \boxed{x = 3 \sqrt{2} }[/tex]
