How to show that

woo · **Joined:** Fri, 13 Dec 2013 14:47:37 UTC **Posts:** 200

Given that $\gamma$ ,

,

, are positive constants, that $\gamma^2-4km<0$ and that $\frac{\gamma^2}{4km}$ is small, how to show that $(1-\frac{\gamma^2}{4km})^{-1/2}\approx1+\frac{\gamma^2}{8km}$ ? I try by multiplying both the numerator and denominator by $(1+\frac{\gamma^2}{4km})^{1/2}$ but unsuccessful. Also $(1+\frac{\gamma^2}{8km})^{-2}=(1+\frac{\gamma^2}{4km}+\frac{\gamma^4}{64k^2m^2})^{-1}=\frac{64k^2m^2}{64k^2m^2+16km\gamma^2+\gamma^4}$ it seem they are not very close to each other.

S.O.S. Mathematics CyberBoard

How to show that

Who is online