The authors consider the problem \[ -\Delta u - \mu {u\over{| x| ^2}} = {{| u| ^{2^*(s)-2}}\over{| x| ^s}}u + \lambda u \quad\text{in}\quad \Omega, \qquad u = 0 \quad\text{on}\quad \partial\Omega, \leqno(*) \] where \(\Omega\) is a smooth bounded domain in \({\mathbb R}^N\), \(N\geq 3\), containing the origin, \(\lambda>0\), \(0\leq \mu 0\) the problem \((*)\) has a nontrivial solution \(u\in H_0^1(\Omega)\) with energy in the range \((0,{{2-s}\over{2(N-s)}} (A_{\mu,s})^{(N-s)/(2-s)})\), where \[ A_{\mu,s} = \inf_{ u\in H_0^1(\Omega)\backslash\{0\} } \int_\Omega \left( | \nabla u| ^2 - \mu{{| u| ^2}\over{| x| ^2}} \right)dx \bigg/ \left( \int_\Omega {{| u| ^{2^*(s)}}\over{| x| ^s}}\,dx \right)^{2/2^*(s)}. \] The case \(s=0\) was proved previously by \textit{D.~Cao} and \textit{P.~Han} [J. Differ. Equ. 205, 521--537 (2004; Zbl 1154.35346)].