If the original instance is a positive one, then the optimal value is equal to c(x), but this implies that the approximal solution has measure smaller then r times the optimal solution, which is equal to r times c(x).But since we are assuming that r is smaller then (1+g), then we have that the measure of the optimal solution is smaller then c(x)(1+g).
On the other hand if the original instance is negative instance, then the optimal solution must be equal or greater then c(x)(1+g). But since this is the optimal solution, clearly every solution must be greater than this value.
So we have derive a polynomial time algorithm that allows us to solve P2 in polynomial time.
