the inequality $\sum_{sym}\frac{a}{\sqrt{a^2 + kbc}} \geq \frac{3}{\sqrt{1+k}}$
is true for all $a, b, c > 0$ $iff$ $k \geq 8$.
comment:
A Generalized Inequality
-
Sazid Akhter Turzo
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Prove that...
the inequality $\sum_{sym}\frac{a}{\sqrt{a^2 + kbc}} \geq \frac{3}{\sqrt{1+k}}$
is true for all $a, b, c > 0$ $iff$ $k \geq 8$.
comment:
the inequality $\sum_{sym}\frac{a}{\sqrt{a^2 + kbc}} \geq \frac{3}{\sqrt{1+k}}$
is true for all $a, b, c > 0$ $iff$ $k \geq 8$.
comment:
-
Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: A Generalized Inequality
Solution(s):One huge solution was given in the Compendium.
Another one can be found using Holder.(Of course, this is my solution
)
The third solution needs to use Jensen.
See this:
http://www.artofproblemsolving.com/Foru ... 38&t=17451
Another one can be found using Holder.(Of course, this is my solution
)The third solution needs to use Jensen.
See this:
http://www.artofproblemsolving.com/Foru ... 38&t=17451
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