_^g2HEY NUPUR , DONT WORRY , MAIN HOON NAA................

(KIDDING).....

NOW ,look...........

use conservation of  energy ........

initial energy= -GM_{^{1 m}}/(d/2) -GM₂  m/(d/2) + 1/2 m v²

⁽  as mass m is d/2 apart from moon as well as earth , therefore , gravitational energy is there , and mass is given a velocity v , therefore kinetic energy is also present.....RIGHT)

NOW ,

FINAL ENERGY= -GM₁  m/$ - GM₂  m/$     ( $--- REPRESENTS INFINITY)

(THERE IS NO KINETIC ENERGY BCOZ AT THAT POINT V=0)

NOW EQUATING , WE GET

  GM₁m/ (d/2) + GM₂ m/(d/2) = 1/2 m V²