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I am working on the last part of a problem now in which I am trying to find what velocity (as a fraction of c) must be traveled from the Earth to Andromeda (a distance of 2.00x10^6 light-years) in order for only 20 years to pass in the reference frame of the rocket. I created my equation and know what I need to do to solve it, but not sure where to employ a certain technique to solve it. My equation is:

(time in rocket frame)^2 = (time in earth frame)^2 - (distance in earth frame)^2

(20 years)^2 = (earth time)^2 - (2.00x10^6)^2

I realize that (earth time) = 2.00x10^6 / velocity

However, the book wants me to use 2 binomial approximations of the form (1+z)^n ~ 1+nz to solve the problem. I am having trouble determining where these can be applied.

Thanks