Question 168652
p =  E^2R/(r+R)^2

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P(r^2+ 2rR +R^2) = E^2R
pr^2 + 2prR + pR^2 = E^2R

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E^2R - pR^2 = pr^2 + 2prR

pR^2 + (2pr-E^2)R +pr^2 = 0

R = [(E^2-2pr) +- sqrt[(E^2-2pr)^2 - 4p(pr^2)]/(2p)

I'll let you take it from there.
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Cheers,
Stan H.