a cylinder is on a rough floor with its axis horizontal. it is touching a vertical wall (also rough). a cross sectional plane perpendicular to axis going through center of mass would be a circle with two points touching wall and floor , both have equal roughness of mu. cylinder masss is W. the question is the maximum couple ( around the axis) that the cylinder could withstand  without slipping.

my approach is as follows

1. freebody diagram with , frictional forces on wall and floor and normal forces  + weight  + couple M
2. resolve forces (2 equations)- M has no contributiion
3. taking moments from centre ( M present)
4 two inequalities for F< mu R  for floor and wall

gives 5 equations ,

5. get all quantities using  3 equations taking one frictional force as parameters
6. plug in  that in two inequalities which will give  X>F>Y inequality
7. from that i got X>y which tells me what my M is

I dont seem to get the book answer which is Wg(mu)(mu+1)/(mu^2+1)

have i missed something?