\(
M=\frac{1+\frac{\sqrt{a^{2}-1}}{\sqrt{a-1}}}{\frac{\sqrt{a-1}-\sqrt{a+1}}{\sqrt{a-1}\sqrt{a+1}}}\div \frac{\sqrt{a+1}}{\sqrt{a^{2}-1}\left ( \sqrt{a-1} -\sqrt{a+1} \right )}
\)
\(
=\frac{\sqrt{a+1}\left ( 1+\sqrt{a^{2}-1} \right )}{\sqrt{a-1}-\sqrt{a+1}}\times \frac{\left ( \sqrt{a-1}-\sqrt{a+1} \right )\sqrt{a-1}}{1}=\sqrt{a^{2}-1}\left ( 1+\sqrt{a^{2}-1} \right )
\)
khi \(
a=5\sqrt{2}\Rightarrow a^{2}=50\Rightarrow a^{2}-1=49
\)
\(
M=\sqrt{49}\left ( 1+\sqrt{49} \right )=7\times 8=56
\)