The scarce spectrum and power resources, the inter-beam interference, together with the high traffic demand, pose new major challenges for the next generation of Very High Throughput Satellite (VHTS) systems. Accordingly, future satellites are expected to employ advanced resource/interference management techniques to achieve high system spectrum efficiency and low power consumption while ensuring user demand satisfaction. This paper proposes a novel demand and interference aware adaptive resource management for geostationary (GEO) VHTS systems. For this, we formulate a multi-objective optimization problem to minimize the total transmit power consumption and system bandwidth usage while matching the offered capacity with the demand per beam. In this context, we consider resource management for a system with full-precoding, i.e., all beams are precoded; without precoding, i.e., no precoding is applied to any beam; and with partial precoding, i.e., only some beams are precoded. The nature of the problem is non-convex and we solve it by jointly using the Dinkelbach and Successive Convex Approximation (SCA) methods. The simulation results show that the proposed method outperforms the benchmark schemes. Specifically, we show that the proposed method requires low resource consumption, low computational time, and simultaneously achieves a high demand satisfaction.