(x+y)*(x+z)*(y+z)>=8xyz

How to show this, I suppose somehow with the AM–GM inequality, but don't know how.

Thank you!

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- Dec 18th 2011, 08:40 AMgotmejerryInequality
(x+y)*(x+z)*(y+z)>=8xyz

How to show this, I suppose somehow with the AM–GM inequality, but don't know how.

Thank you!

- Dec 18th 2011, 09:20 AMprincepsRe: Inequality
- Dec 18th 2011, 09:23 AMgotmejerryRe: Inequality
Thank you!

- Dec 18th 2011, 09:24 AMprincepsRe: Inequality
you are welcome

- Dec 18th 2011, 09:29 AMILikeSerenaRe: Inequality
Just nitpicking...

For x=1, y=-1, z=-1, you get:

$\displaystyle (1-1)(1-1)(-1-1) \ge 8 \cdot 1 \cdot -1 \cdot -1 $

$\displaystyle \Rightarrow 0 \ge 8$

which is a contradiction. :rolleyes: - Dec 18th 2011, 09:32 AMPlatoRe: Inequality
- Dec 18th 2011, 10:03 AMgotmejerryRe: Inequality
Sorry, I forgot that x,y,z are postives:D