MATH 201 Midterm: MATH 201 Exam 3
Document Summary
This test is closed book and closed notes. For full credit show all of your work (legibly!). Each problem is worth 10 points (a total of 50 points): given positive numbers s, t, u, v prove that stuv (s + u)4 + (t + v)4. We recall the arithmetic geometric mean inequality, which we can state in several di erent ways, namely. Starting with the left hand side we have stuv (su)2 + (tv)2. 2 (s + u)4 + (t + v)4. The rst inequality comes from applying the rst form of the agm inequality with x = su and y = tv. The second inequality comes from applying the second form of the agm inequality with x = s and y = u in the rst case and x = t and y = v in the second case. Finally we simplify: fill in the truth table below. Q r (p q) r p (q r)
