- #1
Saitama
- 4,243
- 93
Homework Statement
Let ##a,b,c## be positive real numbers with sum 3. Prove that
[tex]\sqrt{a}+\sqrt{b}+\sqrt{c} \geq ab+bc+ca[/tex]
Homework Equations
AM-GM inequality
The Attempt at a Solution
I don't really know how to start with. We are given ##a+b+c=3##.
Also, ##2(ab+bc+ca)=(a+b+c)^2-(a^2+b^2+c^2)## but this doesn't seem helpful here and I don't see how can I apply the AM-GM inequality here. :(