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$ \begin{aligned}解:原式&=\frac {3\sqrt 2}{3}×\sqrt 2 \\ &=2 \\ \end{aligned}$
$ \begin{aligned}解:原式&=4\sqrt 2-6\sqrt 2-2\sqrt 2+2 \\ &=-4\sqrt{2}+2 \\ \end{aligned}$
$ \begin{aligned} 解:原式&=5-2\sqrt {10}+2-2\sqrt {10} \\ &=7-4\sqrt{10} \\ \end{aligned}$
$ \begin{aligned} 解:原式&=2\sqrt 6-\frac 32+16-2\sqrt 6 \\ &=14\frac{1}{2} \\ \end{aligned}$
解：由数轴可知$b\lt a\lt0\lt c，$$\vert b\vert\gt\vert a\vert，$$\vert b\vert\gt\vert c\vert。$
则$a + b\lt0，$$c - a\gt0，$$b + c\lt0。$
$\begin{aligned}&\sqrt{a^2}-\vert a + b\vert+\sqrt{(c - a)^2}+\vert b + c\vert\\=&-a-(-(a + b))+(c - a)+(-(b + c))\\=&-a+a + b+c - a - b - c\\=&-a\end{aligned}$
解：已知$x=\frac{1}{2 - \sqrt{3}}=\frac{2+\sqrt{3}}{(2 - \sqrt{3})(2+\sqrt{3})}=2+\sqrt{3}，$$\frac{1}{x}=2-\sqrt{3}。$
(1)$x+\frac{1}{x}=2+\sqrt{3}+2-\sqrt{3}=4。$
(2)
$\begin{aligned}&(7 - 4\sqrt{3})x^2+(2 - \sqrt{3})x+\sqrt{3}\\=&(7 - 4\sqrt{3})(2+\sqrt{3})^2+(2 - \sqrt{3})(2+\sqrt{3})+\sqrt{3}\\=&(7 - 4\sqrt{3})(7 + 4\sqrt{3})+(2 - \sqrt{3})(2+\sqrt{3})+\sqrt{3}\\=&49-48 + 4 - 3+\sqrt{3}\\=&2+\sqrt{3}\end{aligned}$
解：原式​$=x^2-4xy + 4y^2+5xy - x^2-4y^2=xy$​，
当​$x = \frac {\sqrt {5}+1}{2}$​，​$y = \frac {\sqrt {5}-1}{2}$​时，
原式​$=\frac {\sqrt {5}+1}{2}×\frac {\sqrt {5}-1}{2}=\frac {(\sqrt {5})^2-1^2}{4}=1$​。
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