Positive numbers $x_1,..., x_k$ satisfy the following inequalities: $$x_1^2+...+ x_k^2 <\frac{x_1+...+x_k}{2} \ \ and \ \ x_1+...+x_k < \frac{x_1^3+...+ x_k^3}{2}$$a) Show that $k > 50$, (3) b) Give an example of such numbers for some value of $k$ (3) c) Find minimum $k$, for which such an example exists. (3)