Školjka

%V0 Determine all real numbers a for which there exists positive reals $x_{1}, \ldots, x_{5}$ which satisfy the relations $\displaystyle \sum_{k=1}^{5} kx_{k}=a,$ $\displaystyle \sum_{k=1}^{5} k^{3}x_{k}=a^{2},$ $\displaystyle \sum_{k=1}^{5} k^{5}x_{k}=a^{3}.$