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CaptainBlack · #7 June 25th, 2007, 09:37 AM

Quote:

Originally Posted by red_dog

For $x,y,z\in\mathbf{R}$ the inequality is not tight.
We have $x^2+y^2+z^2\geq xy+xz+yz\Rightarrow$
$\Rightarrow (x+y+z)^2-2(xy+xz+yz)\geq xy+xz+yz\Rightarrow$
$\Rightarrow xy+xz+yz\leq \frac{1}{3}<\frac{1}{2}$ .
The equality stands for $x=y=z=\frac{1}{3}$ .

You need to fill in some of the detail so others can follow this more easily.

RonL