Question

значение выражения

 

$(frac{x^{-0.75}-x^{-1.25}}{x^{-0.75}-x^{-0.25}})^{-1}$

 

 

при а = 2.5 * 10^-3

Answer 1

при а = 2.5 * 10^-3:

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

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