Problem:
What is the value of x if β£xβ1β£=β£xβ2β£?
Answer Choices:
A. β21β
B. 21β
C. 1
D. 23β
E. 2
Solution:
The equation implies that either
xβ1=xβ2 or xβ1=β(xβ2)
The first equation has no solution, and the solution to the second equation is x=(D)23ββ.
OR
Since β£xβaβ£ is the distance of x from a,x must be equidistant from 1 and 2. Hence x=23β.
Answer: Dβ.
The problems on this page are the property of the MAA's American Mathematics Competitions