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第124頁

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A
解：原式?$=\sqrt {40×10}$?
?$ =\sqrt {400}$?
?$ =20$?
解：原式?$=\sqrt {50÷2}$?
?$ =\sqrt {25}$?
?$ =5$?
解：原式?$=\sqrt {2}+2\sqrt {2}-6\sqrt {2}$?
?$ =-3\sqrt {2}$?
解：原式?$=3-2\sqrt {11}+3\sqrt {11}-22$?
?$ =\sqrt {11}-19$?
解：原式?$=(\sqrt {2})2-(\sqrt {5})2$?
?$ =2-5$?
?$ =-3$?
解：原式?$=3-2\sqrt {6}+2$?
?$ =5-2\sqrt {6}$?
解：原式?$=8\sqrt {3}×\frac {\sqrt {2}}{2}÷5\sqrt {3}$?
?$ =4\sqrt {6}×\frac {\sqrt {3}}{15}$?
?$ =\frac {4\sqrt {2}}{5}$?
解：原式?$=14a\sqrt {2a}-4a2×\frac {1}{2\sqrt {2a}}+7a\sqrt {2a}$?
?$ =14a\sqrt {2a}-a\sqrt {2a}+7a\sqrt {2a}$?
?$ =20a\sqrt {2a}$?
解：將?$a=2，$??$b=-8，$??$c=5$?代入得：
原式?$=\frac {-8+\sqrt {64-4×2×5}}{2×2}=\frac {8+2\sqrt {6}}{4} =2+\frac {\sqrt {6}}{2}$?
解：原式?$=a2+2ab+b2+(2a2+ab-2ab-b2)-3a2=ab$?
將?$a=2+\sqrt {3}，$??$b=2-\sqrt {3}$?代入原式得：
原式?$=(2+\sqrt {3})(2-\sqrt {3}) =4-3 =1$?
解：菱形的邊長為?$\sqrt {96}÷4=\sqrt {6}(\mathrm {cm})$?
∵?$∠DAB = 120°$?
∴?$∠DAO= 60°$?
∴?$OA=\frac {\sqrt {6}}{2}\mathrm {cm}，$??$OD=\frac {3\sqrt {2}}{2}\mathrm {cm}$?
∴?$AC=\sqrt {6}(\mathrm {cm})，$??$BD = 3\sqrt {2}(\mathrm {cm})$?
∴?$S=\frac {1}{2}×AC×BD=3\sqrt {3}(\mathrm {cm}2)$?
解：∵?$(a+\frac {1}{a})2=a2+2+\frac {1}{a2}=10$?
∴?$a2+\frac {1}{a2}=8$?
?$(a-\frac {1}{a})2=a2-2+\frac {1}{a2}=6$?
∴?$a-\frac {1}{a}=±\sqrt {6}$?
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