1. The problem statement, all variables and given/known data Suppose that a and b are nonzero real numbers. Prove that if a< 1/a < b < 1/b then a<-1. 2. Relevant equations Givens: a and b are nonzero real numbers, a< 1/a < b < 1/b, and a≥-1. Goal: Arrive at a contradiction. 3. The attempt at a solution Scratch work: First establish whether a<0 or a>0. Case i.) a>0 and Case ii.) a<0 Case i). a>0. a( a<1/a) ⇒ a2<1 and a(a≥-1) ⇒ a2≥-a. However a2≥0 and -a<0. Therefore a>0 contradicts the fact that a is at leas greater than or equal to -1. Is the argument sound? Thanks for the feedback!