The goal of this exercise is threefold: 1. To show that some sets that occur in optimization can be described in a compact manner by just one nonlinear inequality. 2. At the same time, it takes many linear inequalities to describe the same set. 3. At the same time, if we use extra variables, we can describe the same set with a lot fewer linear inequalities. 1. (40 points) The n dimensional mystery set is n M(n) = {x R" : \xil