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第109頁

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解：原式???$=\sqrt 2-1-1+2(\sqrt 3+1)-\sqrt 2$???

???$ =2\sqrt 3+2-1-1+(\sqrt 2-\sqrt 2)$???

???$ =2\sqrt 3$???

解：原式???$=2x\sqrt x+\sqrt {xy}-(x\sqrt x-5\sqrt {xy})$???

???$ =3x\sqrt x+6\sqrt {xy}$???

當(dāng)???$x=\frac 12，$??????$y=4$???時(shí)，

原式???$=3×\frac 12\sqrt {\frac 12}+6\sqrt {\frac 12×4}=\frac {25\sqrt 2}4$???

解：???$(1)S_{△ABC}=2×2×\frac 12=2$???

???$ (2)$???設(shè)點(diǎn)???$A$???到???$BC$???邊的距離為???$h。$???

∴???$\frac 12×h×\sqrt {20}=2$???

解得：???$h=\frac {2\sqrt 5}5$???

∴點(diǎn)???$A$???到???$BC$???邊的距離為???$\frac {2\sqrt 5}5.$???

解：???$a+b=\frac {\sqrt 5+2+\sqrt 5-2}{(\sqrt 5+2)(\sqrt 5-2)}=2\sqrt 5$???

???$ ab=\frac 1{(\sqrt 5+2)(\sqrt 5-2)}=1$???

∴原式???$=\frac {a^2+b^2}{ab}=\frac {(a+b)^2-2ab}{ab}=\frac {20-2}1=18$???

解：???$(1)$???由題意得???$S=(6\sqrt 3)^2-4×(\sqrt 3)^2=96(\ \mathrm {cm^2})$???

???$(2)V=(6\sqrt 3-2\sqrt 3)(6\sqrt 3-2\sqrt 3)\sqrt ×\sqrt 3=48\sqrt 3(\ \mathrm {cm^2}).$???

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