第142页 - 江苏版实验班提优训练数学八年级上下册答案

$解:由题意，得x= (\sqrt{3}+\sqrt{2})²=5+2\sqrt{6}，$

$y=(\sqrt{3}- \sqrt{2})²=5-2\sqrt{6}，$

$∴x+y=10，x-y=4\sqrt{6}，xy=1.\ $

$∴原式= \frac {x-y}{xy(x+y)}= \frac{4\sqrt{6}}{1×10}=\frac {2\sqrt {6} }{5}.$

$ \begin{aligned}解:(1)①原式&=\frac{4×(\sqrt{13}+3)}{(\sqrt{13}-3)(\sqrt{13}+3)} \\ &= \sqrt{13}+3. \\ ②原式&=\frac {\sqrt {n} -\sqrt {n-2} }{(\sqrt {n} +\sqrt {n-2} )(\sqrt {n} -\sqrt {n-2} )} \\ &=\frac {\sqrt{n}- \sqrt{n-2}}{2}. \\ \end{aligned}$

$(2)原式=\frac{1}{3}(\sqrt{5}- \sqrt{2}+ \sqrt{8}- \sqrt{5}+ \sqrt{11}- \sqrt{8}$

$+···+\sqrt{3n+2}- \sqrt{3n-1})( \sqrt{3n+2}+\sqrt {2} ) $

$ \begin{aligned} ~~~~~~~~~~~~~~&=\frac{1}{3}( \sqrt{3n+2}-\sqrt {2} )( \sqrt{3n+2}+\sqrt{2}) \\ &=n. \\ \end{aligned}$

m²+5n²

2mn

21

4

1

2

$解:由(1)知，a=m²+5n²，6=2mm，$

$∴mm=3.$

$ ∵a、m、n均为正整数，$

$∴m=1，n=3或m=3，n=1.$

$ 当m=1，n=3时，a=1²+5×3²=46；$

$ 当m=3，n=1时，a=3²+5×1²=14.$

$ 综上所述，a的值为14或46.$