Problem:
Assuming aξ =3,bξ =4, and cξ =5, what is the value in simplest form of the following expression?
5βcaβ3ββ
3βabβ4ββ
4βbcβ5β
Answer Choices:
A. β1
B. 1
C. 60abcβ
D. abc1ββ601β
E. 601ββabc1β
Solution:
If xξ =y, then
yβxxβyβ=β1
We use this fact to simplify the original expression:
===β5βcaβ3ββ
3βabβ4ββ
4βbcβ5β3βaaβ3ββ
4βbbβ4ββ
5βccβ5ββ1β
β1β
β1(A)β1ββ
The problems on this page are the property of the MAA's American Mathematics Competitions