Problem: If it is known that log2​a+log2​b≦6 and that ab is a maximum, then the least value that can be taken on by a+b is:
Answer Choices:
A. 26​
B. 6
C. 82​
D. 16
E. none of these
Solution:
Since log2​a+log2​b≦6,log2​ab≦6. ∴ab≦26=64. Since ab is a maximum, ab= 64. Therefore, the least value that can be taken on by a+b is 8+8=16. [ff P=ab,
the least value of a+b is P​+P​=2P​. One way of proving this theorem is to consider the minimum value of f=a2−aS+P where S=a+b.