I calculated the answer to be
v2=4G[m1/r1 + m2/r2]
Please confirm
The masses and radii of earth and moon are M1, R1 and M2, R2 respectively, their centres are r distance apart, find minimum speed with which particle of mass m should be projected from a mid way between 2 centres so as to escape to infinity.
The main-trick lies in the fact, that total energy of an open-path-system needs to be negative, see if u can get it from there....