So did you get the equations right in part a? I'll assume you did.
Rearranging them a little gives:
$\displaystyle u-v=\frac{M}{m}V$
and
$\displaystyle u^2-v^2=\frac{M}{m}V^2$
Factorise the left side of the second equation and everything will become easy.
this is how i solve can u point out at what am i doing wrong
v=V-u equation 2
mv+MV=mu equation 1
multiplying eq 2 by M
we get Mv=MV+Mu equation 3
adding equation 3 and 1 we get
v=(m-M)u/(m+M) equation 4
multiplying eq 2 by m
mv=mV-mu equation 5
adding equation 5 and 1 we get
V=2mu/(m+M)
plugging these values in the energy loss in kinectic energy
mu^2{1-(m+M)2-4mM/(m+M)^2 i get 0/(m+M)^2 i know i am close but what i am doing wrong??