Question

Значение выражения при а = 2.5 * 10^-3

Answer 1

при а = 2.5 * 10^-3:

$(\frac{x^{-0.75}-x^{-1.25}}{x^{-0.75}-x^{-0.25}})^{-1}=\\\\ (\frac{1-x^{-0.5}}{1-x^{0.25}})^{-1}=\\\\ \frac{1-x^{0.25}}{1-x^{-0.5}}=\\\\ \frac{(1-x^{0.25})*x^{0.5}}{x^{0.5}-1}=\\\\ \frac{(1-x^{0.25})*x^{0.5}}{(x^{0.25}-1)*(1+x^{0.25})}=\\\\ \frac{-x^{0.5}}{1+x^{0.25}}=\\\\ \frac{-\sqrt{x}}{1+\sqrt[4] {x}}=\\\\ \frac{-\sqrt{2.5*10^{-3}}}{1+\sqrt[4] {2.5*10^{-3}}}=\\\\ \frac{-\sqrt{0.0025}}{1+\sqrt[4] {0.0025}}=\\\\ \frac{-0.05}{1+\sqrt {0.05}}=\\\\$

$\frac{-0.05*(1-\sqrt{0.05})}{(1+\sqrt {0.05})*(1-\sqrt{0.05})}=\\\\ \frac{-0.05*(1-\sqrt{0.05})}{1^2-(\sqrt {0.05})^2}=\\\\ \frac{-0.05*(1-\sqrt{0.05})}{1-0.05}=\\\\ \frac{-0.05*(1-\sqrt{0.05})}{0.05}=\\\\ -(1-\sqrt{0.05})=\sqrt{0.05}-1=0.1\sqrt{5}-1$