Question

Помогите с выполнением заданий 19,20,21

Answer 1

$1) \frac{6+\sqrt{6}}{\sqrt{30}+\sqrt{5}}=\frac{(\sqrt{6})^{2}+\sqrt{6}}{\sqrt{6*5}+\sqrt{5}}=\frac{\sqrt{6}(\sqrt{6}+1)}{\sqrt{5}(\sqrt{6}+1)}=\frac{\sqrt{6}}{\sqrt{5}}=\frac{\sqrt{30}}{5}\\\\2) \frac{4a^{2}+4a\sqrt{b}+b}{4a^{2}-b} =\frac{(2a)^{2}+4a\sqrt{b}+(\sqrt{b})^{2}}{(2a)^{2}-(\sqrt{b})^{2}}=\frac{(2a+\sqrt{b})^{2}}{(2a-\sqrt{b})(2a+\sqrt{b})}=\frac{2a+\sqrt{b}}{2a-\sqrt{b}}$

$3) x^{2} =\sqrt{\sqrt{10}-3}*\sqrt{\sqrt{10}+3}\\\\x^{2} =\sqrt{(\sqrt{10}-3)(\sqrt{10}+3)} \\\\x^{2} =\sqrt{10-9}\\\\x^{2} =1 \\\\x_{1}=1\\\\x_{2}=-1 \\\\ \frac{S}{t}=\frac{1}{v}+2\\\\\frac{S}{t}=\frac{1+2v}{v}\\\\t=\frac{S*v}{1+2v}$