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#1

$Old$ September 4th, 2008, 10:04 AM

ballrideball $ballrideball is offline$

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$Default$ inequality with three vars

Prove that:
$3(-2zy+z^{4/3}y^{2/3}+y^{4/3}z^{2/3})+4(z-x)^2+4(x-y)^2+(y-z)^2\geq0$
for all $x,y,z\in R_{+}$
It's very hard task and I can't get through it.

[I've corrected it, there was a mistake]

Last edited by ballrideball; September 4th, 2008 at 01:32 PM. Reason: mistake

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#2

$Old$ September 5th, 2008, 12:34 AM

ballrideball $ballrideball is offline$

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Could anyone help me?

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#3

$Old$ September 7th, 2008, 01:24 PM

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kezman $kezman is offline$

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$Default$

$4(z-x)^2+4(x-y)^2+(y-z)^2$
This is positive

$(-2z+z^{4/3}y^{2/3}+y^{4/3}z^{2/3})$
This is equal to

$(z^{2/3}y^{1/3}-y^{2/3}z^{1/3})^2$
That is positive

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