We evaluate different algorithms and the use of a mixed-precision approach for the solution of Algebraic Riccati Equations (AREs). The mixed-precision method obtains an approximation to the solution using single-precision arithmetic and then, this approximation is improved via a cheap iterative refinement. Some numerical results show that the mixed-precision solver reports time and energy savings and also provides similar or even more accurate solutions than well-known methods like the Sign Function or SDA on CPU-GPU platforms.