Ответ:
[tex]a)\ \ (\sqrt{15}+\sqrt{10})\cdot 2\sqrt5-5\sqrt{12}=\sqrt{15}\cdot 2\sqrt5+\sqrt{10}\cdot 2\sqrt5-5\sqrt{12}=\\\\=2\sqrt{15\cdot 5}+2\sqrt{10\cdot 5}-5\sqrt{12}=2\cdot 5\sqrt3+2\cdot 5\sqrt2-5\cdot 2\sqrt3=10\sqrt{2}[/tex]
[tex]\displaystyle b)\ \ \frac{2\sqrt{70}-2\sqrt{28}}{3\sqrt{35}-3\sqrt{14}}=\frac{2(\sqrt{2\cdot 35}-\sqrt{2\cdot 14})}{3(\sqrt{35}-\sqrt{14})}=\frac{2\sqrt2(\sqrt{35}-\sqrt{14})}{3(\sqrt{35}-\sqrt{14})}=\frac{2\sqrt{2}}{3}[/tex]
[tex]c)\ \ (2\sqrt{12}-3\sqrt{3})^2=\Big(2\cdot 2\sqrt3-3\sqrt3\Big)^2=\Big(\sqrt{3}\cdot (4-3)\Big)^2=(\sqrt3)^2=3[/tex]
[tex]\displaystyle d)\ \ \frac{10-5\sqrt3}{10+5\sqrt3}+\frac{10+5\sqrt3}{10-5\sqrt3}=\frac{(10-5\sqrt3)^2+(10+5\sqrt3)^2}{(10+5\sqrt3)(10-5\sqrt3)}=\\\\\\=\frac{100-100\sqrt3+25\cdot 3+100+100\sqrt3+25\cdot 3}{100-25\cdot 3}=\frac{200+150}{25}=\frac{350}{25}=14[/tex]
[tex]\displaystyle\bf\\1)\\\\\Big(\sqrt{15}+\sqrt{10} }\Big) \cdot 2\sqrt{5} -5\sqrt{12} =\sqrt{15} \cdot 2\sqrt{5} +\sqrt{10} \cdot 2\sqrt{5} -5\sqrt{4\cdot 3}=\\\\=2\sqrt{5\cdot 3\cdot 5}+2\sqrt{5\cdot 2\cdot 5} -5\cdot 2\cdot \sqrt{3} =2\cdot 5\cdot\sqrt{3} +2\cdot 5\cdot \sqrt{2} -10\sqrt{3} =\\\\=10\sqrt{3} +10\sqrt{2} -10\sqrt{3} =10\sqrt{2} \\\\Otvet \ : \ 10\sqrt{2 }[/tex]
[tex]\displaystyle\bf\\2)\\\\\frac{2\sqrt{70} -2\sqrt{28} }{3\sqrt{35}-3\sqrt{14} } =\frac{2(\sqrt{7\cdot10} -\sqrt{7\cdot 4} )}{3(\sqrt{7\cdot 5} -\sqrt{7\cdot 2} )} =\frac{2\sqrt{7}(\sqrt{10}-2) }{3\sqrt{7} (\sqrt{5} -\sqrt{2} )} =\\\\\\=\frac{2\sqrt{2}(\sqrt{5} -\sqrt{2} ) }{3(\sqrt{5} -\sqrt{2} )} =\frac{2\sqrt{2} }{3} \\\\\\Otvet \ : \ \frac{2\sqrt{2} }{3}[/tex]
[tex]\displaystyle\bf\\3)\\\\(2\sqrt{12} -3\sqrt{3})^{2} =(2\sqrt{4\cdot 3} -3\sqrt{3} )^{2} =(2\cdot 2\sqrt{3} -3\sqrt{3} )^{2} =\\\\=(4\sqrt{3} -3\sqrt{3} )^{2} =(\sqrt{3} )^{2} =3\\\\Otvet \ : \ 3\\\\\\4)\\\\\frac{10-5\sqrt{3} }{10+5\sqrt{3} } +\frac{10+5\sqrt{3} }{10-5\sqrt{3} } =\frac{(10-5\sqrt{3})\cdot(10-5\sqrt{3} )+(10+5\sqrt{3})\cdot(10+5\sqrt{3} ) }{(10+5\sqrt{3})\cdot(10-5\sqrt{3} ) } =\\\\\\=\frac{100-100\sqrt{3} +75+100+100\sqrt{3} +75}{100-75} =\frac{350}{25} =14\\\\\\Otvet: 14[/tex]
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Ответ:
[tex]a)\ \ (\sqrt{15}+\sqrt{10})\cdot 2\sqrt5-5\sqrt{12}=\sqrt{15}\cdot 2\sqrt5+\sqrt{10}\cdot 2\sqrt5-5\sqrt{12}=\\\\=2\sqrt{15\cdot 5}+2\sqrt{10\cdot 5}-5\sqrt{12}=2\cdot 5\sqrt3+2\cdot 5\sqrt2-5\cdot 2\sqrt3=10\sqrt{2}[/tex]
[tex]\displaystyle b)\ \ \frac{2\sqrt{70}-2\sqrt{28}}{3\sqrt{35}-3\sqrt{14}}=\frac{2(\sqrt{2\cdot 35}-\sqrt{2\cdot 14})}{3(\sqrt{35}-\sqrt{14})}=\frac{2\sqrt2(\sqrt{35}-\sqrt{14})}{3(\sqrt{35}-\sqrt{14})}=\frac{2\sqrt{2}}{3}[/tex]
[tex]c)\ \ (2\sqrt{12}-3\sqrt{3})^2=\Big(2\cdot 2\sqrt3-3\sqrt3\Big)^2=\Big(\sqrt{3}\cdot (4-3)\Big)^2=(\sqrt3)^2=3[/tex]
[tex]\displaystyle d)\ \ \frac{10-5\sqrt3}{10+5\sqrt3}+\frac{10+5\sqrt3}{10-5\sqrt3}=\frac{(10-5\sqrt3)^2+(10+5\sqrt3)^2}{(10+5\sqrt3)(10-5\sqrt3)}=\\\\\\=\frac{100-100\sqrt3+25\cdot 3+100+100\sqrt3+25\cdot 3}{100-25\cdot 3}=\frac{200+150}{25}=\frac{350}{25}=14[/tex]
[tex]\displaystyle\bf\\1)\\\\\Big(\sqrt{15}+\sqrt{10} }\Big) \cdot 2\sqrt{5} -5\sqrt{12} =\sqrt{15} \cdot 2\sqrt{5} +\sqrt{10} \cdot 2\sqrt{5} -5\sqrt{4\cdot 3}=\\\\=2\sqrt{5\cdot 3\cdot 5}+2\sqrt{5\cdot 2\cdot 5} -5\cdot 2\cdot \sqrt{3} =2\cdot 5\cdot\sqrt{3} +2\cdot 5\cdot \sqrt{2} -10\sqrt{3} =\\\\=10\sqrt{3} +10\sqrt{2} -10\sqrt{3} =10\sqrt{2} \\\\Otvet \ : \ 10\sqrt{2 }[/tex]
[tex]\displaystyle\bf\\2)\\\\\frac{2\sqrt{70} -2\sqrt{28} }{3\sqrt{35}-3\sqrt{14} } =\frac{2(\sqrt{7\cdot10} -\sqrt{7\cdot 4} )}{3(\sqrt{7\cdot 5} -\sqrt{7\cdot 2} )} =\frac{2\sqrt{7}(\sqrt{10}-2) }{3\sqrt{7} (\sqrt{5} -\sqrt{2} )} =\\\\\\=\frac{2\sqrt{2}(\sqrt{5} -\sqrt{2} ) }{3(\sqrt{5} -\sqrt{2} )} =\frac{2\sqrt{2} }{3} \\\\\\Otvet \ : \ \frac{2\sqrt{2} }{3}[/tex]
[tex]\displaystyle\bf\\3)\\\\(2\sqrt{12} -3\sqrt{3})^{2} =(2\sqrt{4\cdot 3} -3\sqrt{3} )^{2} =(2\cdot 2\sqrt{3} -3\sqrt{3} )^{2} =\\\\=(4\sqrt{3} -3\sqrt{3} )^{2} =(\sqrt{3} )^{2} =3\\\\Otvet \ : \ 3\\\\\\4)\\\\\frac{10-5\sqrt{3} }{10+5\sqrt{3} } +\frac{10+5\sqrt{3} }{10-5\sqrt{3} } =\frac{(10-5\sqrt{3})\cdot(10-5\sqrt{3} )+(10+5\sqrt{3})\cdot(10+5\sqrt{3} ) }{(10+5\sqrt{3})\cdot(10-5\sqrt{3} ) } =\\\\\\=\frac{100-100\sqrt{3} +75+100+100\sqrt{3} +75}{100-75} =\frac{350}{25} =14\\\\\\Otvet: 14[/tex]