Problem:
Nonzero real numbers , and satisfy and . How many of the following inequalities must be true?
(I)
(II)
(III)
(IV)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that , so inequality I is true. If , and , then none of the other three inequalities is true.
The problems on this page are the property of the MAA's American Mathematics Competitions