Finally solved it myself.
now substituting into eqn3
Dumping the smallest terms:
I need to solve the equations:
First I try adding and subtracting the two equations to get:
But I can make no real progress from there.
Now the context of the question means that:
, and I am more than happy to make a few aproximations. I expect the binomial aproximation may be useful.
The required solution is:
I have posted the whole question on Physics help forum at: