Problem:
Which of the following is equal to 9−62​​+9+62​​?
Answer Choices:
A. 32​
B. 26​
C. 272​​
D. 33​
E. 6
Solution:
Let k=9−62​​+9+62​​. Squaring both sides and simplifying results in
k2​=9−62​+2(9−62​)(9+62​)​+9+62​=18+281−72​=18+29​=24​
Because k>0,k=(B)26​​.
The problems on this page are the property of the MAA's American Mathematics Competitions