Решение №16897: \(\left ( \frac{3^{\frac{3}{2}}+\frac{1}{8}z^{\frac{3}{5}}}{3+\sqrt{3}\sqrt[5]{z}+\frac{1}{4}\sqrt[5]{z^{2}}}+\frac{3\sqrt{3}\sqrt[5]{z}}{2\sqrt{3}+\sqrt[5]{z}} \right )^{-1}:\frac{1}{2\sqrt{12}+\sqrt[5]{32z}}=\left ( \frac{24\sqrt{3}+\sqrt[5]{z^{3}}}{24+8\sqrt{3}\sqrt[5]{z}+2\sqrt[5]{z^{2}}}+\frac{3\sqrt{3}\sqrt[5]{z}}{2\sqrt{3}+\sqrt[5]{z}} \right )^{-1}:\frac{1}{2\left ( 2\sqrt{3}+\sqrt[5]{z} \right )}=\left ( \frac{\left ( 2\sqrt{3}+\sqrt[5]{z} \right )^{2}}{2\left ( 2\sqrt{3}+\sqrt[5]{z} \right )} \right )^{-1}\cdot 2\left ( 2\sqrt{3}+\sqrt[5]{z}\right ) =\frac{2}{2\sqrt{3}+\sqrt[5]{z}}\cdot 2\left ( 2\sqrt{3}+\sqrt[5]{z} \right )=4\)

Ответ: 4

Решение №16898: \(\frac{\sqrt{\frac{abc+4}{a}+4\sqrt{\frac{bc}{a}}}}{\sqrt{abc}+2}=\frac{\sqrt{\frac{abc+4}{a}+\frac{4\sqrt{bc}}{\sqrt{a}}}}{\sqrt{abc}+2}=\frac{\sqrt{\frac{abc+4\sqrt{abc}+4}{a}}}{\sqrt{abc}+2}=\frac{\sqrt{\frac{\left ( \sqrt{abc}+2 \right )^{2}}{a}}}{\sqrt{abc}+2}=\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{0.04}}=\frac{1}{0.2}=5\)

Ответ: 5

Решение №16899: \(\frac{\left ( a^{2}-b^{2} \right )\left ( a^{2}+\sqrt[3]{b^{2}}+a\sqrt[3]{b} \right )}{a\sqrt[3]{b}+a\sqrt{a}-b\sqrt[3]{b}-\sqrt{ab^{2}}}:\frac{a^{3}-b}{a\sqrt[3]{b}-\sqrt[6]{a^{3}b^{2}}-\sqrt[3]{b^{2}}-a\sqrt{a}}=\frac{\left ( a-b \right )\left ( a+b \right )\left ( a^{2}+a\sqrt[3]{b}+\sqrt[3]{b^{2}} \right )}{a\left ( \sqrt{a}+\sqrt[3]{b} \right )-b\left ( \sqrt{a}+\sqrt[3]{b} \right )}:\frac{a^{3}-b}{a\left ( \sqrt{a}+\sqrt[3]{b} \right )-\sqrt[3]{b}\left ( \sqrt{a}+\sqrt[3]{b} \right )}=\frac{\left ( a+b \right )\left ( a^{2}+a\sqrt[3]{b}+\sqrt[3]{b^{2}} \right )}{\sqrt{a}+\sqrt[3]{b}}\cdot \frac{\left ( \sqrt{a}+\sqrt[3]{b} \right )\left ( a-\sqrt[3]{b} \right )}{\left ( a-\sqrt[3]{b} \right )\left ( a^{2}+a\sqrt[3]{b}+\sqrt[3]{b^{2}} \right )}=a+b=4.91+0.09=5\)

Ответ: 5

Решение №16900: \(\left ( \sqrt{25-x^{2}}-\sqrt{15-x^{2}} \right )\left ( \sqrt{25-x^{2}}+\sqrt{15-x^{2}} \right )=2\left ( \sqrt{25-x^{2}}+\sqrt{15-x^{2}} \right ) 25-x^{2}-15+x^{2}=2\left (\sqrt{25-x^{2}}+\sqrt{15-x^{2}} \right ), \sqrt{25-x^{2}}+\sqrt{15-x^{2}}=5\)

Ответ: 5

Решение №16901: \(\left ( x^{4}-7x^{2}+1 \right )^{-2}\cdot \left ( \left ( x^{2}+\frac{1}{x^{2}} \right )^{2}-14\left ( x+\frac{1}{x} \right )^{2}+77 \right )^{\frac{1}{2}}=\frac{1}{\left ( x^{4}-7x^{2}+1 \right )^{2}}\cdot \left ( \left ( x+\frac{1}{x} \right )^{4} -18\left ( x+\frac{1}{x} \right )^{2}+81\right )=\frac{1}{\left ( x^{4}-7x^{2}+1 \right )^{2}}\cdot \sqrt{\left ( \left ( x+\frac{1}{x} \right )^{2}-9 \right )^{2}}=\frac{1}{\left ( x^{4}-7x^{2}+1 \right )^{2}}\cdot \frac{\left ( x^{4}-7x^{2}+1 \right )^{2}}{x^{4}}=\frac{1}{x^{4}}=\frac{1}{\left ( \frac{\sqrt[4]{125}}{5} \right )^{4}}=5\)

Ответ: 5

Решение №16902: \(\left ( \frac{9}{a+8}-\frac{a^{\frac{1}{3}}+2}{a^{\frac{2}{3}}-2a^{\frac{1}{3}}+4} \right )\frac{a^{\frac{4}{3}}+8a^{\frac{1}{3}}}{1-a^{\frac{2}{3}}}+\frac{5-a^{\frac{2}{3}}}{1+a^{\frac{1}{3}}}=\frac{\left ( 3-a^{\frac{1}{3}}-2 \right )\left ( 3+a^{\frac{1}{3}}+2 \right )}{a+8}\cdot \frac{a^{\frac{1}{3}}\left ( a+8 \right )}{\left ( 1-a^{\frac{1}{3}} \right )\left ( 1+a^{\frac{1}{3}} \right )}+\frac{5-a^{\frac{2}{3}}}{1+a^{\frac{1}{3}}}=\frac{5a^{\frac{1}{3}}+a^{\frac{2}{3}}+5-a^{\frac{2}{3}}}{1+a^{\frac{1}{3}}}=\frac{5a^{\frac{1}{3}}+5}{1+a^{\frac{1}{3}}}=5\)

Ответ: 5

Решение №16903: \(\frac{3\sqrt{12}}{\sqrt{45}-4\sqrt{3}}+5\sqrt{2.4}\left ( \sqrt{15}+3 \right )=\frac{3\sqrt{3\cdot 4}}{\sqrt{3\cdot 15}-4\sqrt{3}}+5\sqrt{\frac{12}{5}}\left ( \sqrt{15}+3 \right )=\frac{6}{\sqrt{15}-4}+30+6\sqrt{15}=-6\sqrt{15}-24+30+6\sqrt{15}=6\)

Ответ: 6

Решение №16904: \(\\frac{\left ( 1-y \right )\left ( y+2 \right )}{y^{2}\left ( y+1 \right )^{2}}; y=\frac{\sqrt{3}-1}{2};=\frac{\left (1-\frac{\sqrt{3}-1}{2} \right )\left (\frac{\sqrt{3}-1}{2}+2 \right )}{\left ( \frac{\sqrt{3}-1}{2} \right )^{2}\left ( \frac{\sqrt{3}-1}{2}+1 \right )^{2}}=\frac{\left (\frac{\sqrt{3}-1}{2} \right )^{2}+\frac{\sqrt{3}-1}{2}-2 }{\left (\left ( \frac{\sqrt{3}-1}{2} \right )^{2}+\frac{\sqrt{3}-1}{2} \right )}=\frac{\frac{2-\sqrt{3}}{2}+\frac{\sqrt{3}-1}{2}-2}{\left (\frac{2-\sqrt{3}}{2}+\frac{\sqrt{3}} \right )^{2}}=-\frac{\frac{2-\sqrt{3}+\sqrt{3}-1}{2}-2}{\left ( \frac{2-\sqrt{3}+\sqrt{3}-1}{2} \right )^{2}}=6)

Ответ: 6

Решение №16905: \(8-a+2\sqrt{\left ( 8-a \right )\left ( 5+a \right )}+5+a=25; \sqrt{\left ( 8-a \right )\left ( 5+a \right )}=6\)

Ответ: 6

Решение №16906: \(\frac{\left ( x^{2}-y^{2} \right )\left ( \sqrt[3]{x}+\sqrt[3]{y} \right )}{\sqrt[3]{x^{5}}+\sqrt[3]{x^{2}y^{3}}-\sqrt[3]{x^{2}y^{2}}-\sqrt[3]{y^{5}}}-\left ( \sqrt[3]{xy}+\sqrt[3]{y^{2}} \right )=\frac{\left ( \sqrt[3]{x}-\sqrt[3]{y} \right )\left ( \sqrt[3]{x^{2}}+\sqrt[3]{xy}+\sqrt[3]{y^{2}} \right )}{\sqrt[3]{x}-\sqrt[3]{y}}-\sqrt[3]{xy}-\sqrt[3]{y^{2}}=\sqrt[3]{x^{2}}+\sqrt[3]{xy}+\sqrt[3]{y^{2}}-\sqrt[3]{xy}-\sqrt[3]{y^{2}}=\sqrt[3]{x^{2}}=\sqrt[3]{64^{2}}=4^{2}=16\)

Ответ: 16