The edge cloud provides heterogeneous resources, such as cores, memory, and storage which are then allocated to mobile applications in mobile edge computing, which require multiple types of resources to execute. While current work on mobile edge computing focuses on tasks needing a single resource to run, we investigate the task allocation problem aiming to minimize total energy consumption while considering heterogeneous resource settings. Specifically, we consider the binary computation offloading mode, in which a task executes successfully as a whole. We formulate this as an integer programming problem, and transform that to the two subproblems of the resource allocation and the offloading decision. We propose a heuristic approach to solve the resource allocation subproblem and an approximation algorithm for the offloading decision subproblem. We show that our proposed approximation algorithm is a polynomial time approximation scheme, and hence it achieves a tradeoff between optimality loss and time complexity. Experimental results demonstrate that the performance of our proposed algorithm scales very well for multi-resource allocation in different conditions, and it achieves a good balance of performance and speed.