a)
[tex]|3\sqrt{10} - 8| + |3-\sqrt{10}|-|12-4\sqrt{10}| = 3\sqrt{10}-8 -(3-\sqrt{10})-(-(12-4\sqrt{10}))=\\\\=3\sqrt{10}-8-3+\sqrt{10} +12-4\sqrt{10} =4\sqrt{10}-4\sqrt{10}-11+12=\boxed{1}[/tex]
b)
[tex]|3\sqrt{17}-12| + |4-\sqrt{17}|-|16-4\sqrt{17}| = 3\sqrt{17}-12-(4-\sqrt{17}-(-(16-4\sqrt{17}))=\\\\=3\sqrt{17}-12 - 4+\sqrt{17}+16-4\sqrt{17} =4\sqrt{17}-4\sqrt{17}-16 + 16 =\boxed{ 0}[/tex]
