Posted by Nguyen Song Minh
Edited by Nguyen Trung Tuan
In this post .
Theorem. If such that then . Equal hold iff . Where .
Proof. Cases follows shall occur
a)If , we have equal,
b)If then for some , since hence and we have done!
Corollary . Let such that . Let such that and . Then we have and equal holds iff .
Proof. Because therefore we have done.
Corollary . Let acute triangles and , then we have
Proof. Using Corollary with three functions and .
Now I will use Corollary to solution problem follows
Problem(VMEO). Find minimum of where are three angles of an acute triangle .
Solution. By Corollary we need find the acute triangle such that . This is easy job, in fact, denote common value of fractions above is then by we have .
P/S: We can find minimum of by using Corollary.