Jump to content
Sign in to follow this  
-_-

Lebih lemah dari "Ketaksamaan jangan dibongkar"

Recommended Posts

Tentukan nilai minimum $\frac{a^2 +b^2}{c^2+ab}+\frac{b^2+c^2}{a^2+bc}+\frac{c^2+a^2}{b^2+ac}$, dimana $a,b,c$ bilangan real positif

Share this post


Link to post
Share on other sites
Spoiler

Menurut AMGM $\frac{a^2+b^2}{c^2+ab}+\frac{a^2+c^2}{b^2+ac}+\frac{c^2+b^2}{a^2+bc}\ge 3\Bigl(\frac{(a^2+b^2)(c^2+b^2)(a^2+c^2)}{(c^2+ab)(b^2+ac)(a^2+cb)}\Bigr)^\frac{1}{3}=3\Bigl(\frac{[4,2,0]+2a^2b^2c^2}{\frac{[3,3,0]+[4,1,1]}{2}+2a^2b^2c^2}\bigr)^\frac{1}{3}\ge 3$ menurut Muirhead.

 

 

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this  

×