Question

Помогите пожалуйста, срочно!!! Даю 90 баллов!!!

Answer 1

$11)\sqrt{5-2\sqrt{6} } =\sqrt{3-2\sqrt{6}+2 }=\sqrt{(\sqrt{3})^{2} -2\cdot\sqrt{3}\cdot\sqrt{2}+(\sqrt{2} )^{2}}=\\\\=\sqrt{(\sqrt{3} -\sqrt{2})^{2}}=|\sqrt{3}-\sqrt{2}|=\boxed{\sqrt{3} -\sqrt{2}}\\\\\\12)(\sqrt{9-6\sqrt{2}}-\sqrt{6})^{2} }=\Big(\sqrt{9-6\sqrt{2} }\Big)^{2}-2\cdot\sqrt{9-6\sqrt{2}}\cdot\sqrt{6}+(\sqrt{6})^{2}=\\\\=|9-6\sqrt{2}|-2\cdot\sqrt{3}\cdot\sqrt{3-2\sqrt{2} }+6=9-6\sqrt{2}-2\sqrt{3} \cdot\sqrt{(\sqrt{2}-1)^{2}} +6=$

$=15-6\sqrt{2} -2\sqrt{3}\cdot(\sqrt{2} -1)=15-6\sqrt{2} -2\sqrt{6}+2\sqrt{3}$

$13)\\1)\dfrac{\sqrt{a^{2} -4ab+4b^{2}}}{\sqrt{a^{2}+4ab+4b^{2}}}=\dfrac{\sqrt{(a-2b)^{2}}}{\sqrt{(a+2b)^{2}}} =\dfrac{|a-2b|}{|a+2b|}=\dfrac{2b-a}{a+2b}\\\\\\2)\dfrac{2b-a}{a+2b} -\dfrac{8ab}{a^{2}-4b^{2}}+\dfrac{2b}{a-2b}=\dfrac{2b-a}{a+2b} -\dfrac{8ab}{(a-2b)(a+2b)}+\dfrac{2b}{a-2b}=\\\\=\dfrac{(2b-a)\cdot(a-2b)-8ab+2b\cdot(a+2b)}{(a-2b)(a+2b)} =\\\\=\dfrac{2ab-4b^{2}-a^{2} +2ab-8ab+2ab+4b^{2}}{(a-2b)(a+2b)} =\dfrac{-a^{2}-2ab }{(a-2b)(a+2b)}=$

$=\dfrac{-a(a+2b)}{(a-2b)(a+2b)}=\dfrac{-a}{a-2b}=\dfrac{a}{2b-a}\\\\\\\dfrac{\sqrt{7+4\sqrt{3} }\cdot\sqrt{19-8\sqrt{3}}}{4-\sqrt{3} }-\sqrt{3}=\dfrac{\sqrt{(2+\sqrt{3} )^{2}}\cdot\sqrt{(4-\sqrt{3})^{2}}}{4-\sqrt{3} }-\sqrt{3} =\\\\\\=\frac{(2+\sqrt{3})\cdot(4-\sqrt{3})}{4-\sqrt{3} }-\sqrt{3}=2+\sqrt{3}-\sqrt{3} =2$