[tex]\it a = \dfrac{2}{3+\sqrt{11}} = \dfrac{2}{\sqrt{11} +3} = \dfrac{2(\sqrt{11}-3)}{11-9} = \dfrac{2(\sqrt{11}-3)}{2} =\sqrt{11}-3
\\\;\\ \\\;\\
\sqrt{5\dfrac{1}{2}} = \sqrt{\dfrac{11}{2}} = \dfrac{\sqrt{11}}{\sqrt2}[/tex]
[tex]\it b = 3+\sqrt2\cdot\dfrac{\sqrt{11}}{\sqrt2} = 3+\sqrt{11} =\sqrt{11}+3
\\\;\\ \\\;\\
m_a = \dfrac{a+b}{2} =\dfrac{\sqrt{11}-3+\sqrt{11}+3}{2} = \dfrac{2\sqrt{11}}{2}=\sqrt{11}
[/tex]
