[tex]\sqrt{(2-\sqrt 5)^2}+x\sqrt{9-4\sqrt 5} = x\sqrt{(2+\sqrt 5)^2}-\sqrt{9+4\sqrt 5}\\ \\ |2-\sqrt 5| +x\sqrt{(2-\sqrt 5)^2} = x|2+\sqrt 5| - \sqrt{(2+\sqrt 5)^2} \\ \\ -(2-\sqrt 5) + x|2-\sqrt 5| = x(2+\sqrt 5) - |2+\sqrt 5| \\ \\ \sqrt 5 - 2 + x(\sqrt 5-2) = x(2+\sqrt 5) - (2+\sqrt 5)\\ \\ x(\sqrt 5-2)-x(2+\sqrt 5) = 2-\sqrt 5 - (2+\sqrt 5)\\ \\ x(\sqrt 5 - 2 - 2 +\sqrt 5) = -2\sqrt 5 \\ \\ -4x = -2\sqrt 5\\ \\ \Rightarrow \boxed{x = \dfrac{\sqrt 5}{2}}[/tex]
