the block has sum disp in vertical as well as horizontal direction
vertical disp = l - lcos45
and horizontal disp = lsin45

work done by horizontal force = increase in potential energy

so
F x hor. disp = mg x vert elevation
Fx l/root(r) = mgl ( root(2)-1)/ root(2)
this gives
F = mg( root (2) - 1 )

 

Multiply and divide by ( root (2) + 1 )

and we will get ans as c