How many triples (a, b, c) of real numbers satisfy the equations
ab = c, ac = b, and bc = a ? Choose the correct answer.
A) 2	B) 4	C) 5	D) 6	E) 8
Observe that (0, 0, 0) is a triple as in the problem. Now, if one of a, b and c is 0, then the given   equations imply each of them is 0. So we suppose next that each is non-zero. The equations ab = c   and ac = b imply a2bc = bc so that a2 = 1. Hence, a 2 {1,−1}. Similarly, b 2 {1,−1} and   c 2 {1,−1}. One checks that these imply that either (a, b, c) = (1, 1, 1) or exactly one of a, b and   c is 1 and the other two are −1. These observations lead to the total number of tuples being 5.   correct answer 5
<result>C</result>
How many triples (a, b, c) of real numbers satisfy the equations
ab = c, ac = b, and bc = a ?