Help me, inequality

**mp3qz** · September 4th 2009, 04:56 AM

1./x,y,z>0 & x+y+z=3. Find Min:
$\frac{x^2}{x+2y^3}+\frac{y^2}{y+2z^3}+\frac{z^2}{z+2x^3}$

2./ x,y,z >0. Demonstrate:
$\frac{2\sqrt{x}}{x^3+y^2}+\frac{2\sqrt{y}}{y^3+z^2}+\frac{2\sqrt{z}}{z^3+x^2}\leq\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$

**dhiab** · September 5th 2009, 07:43 PM

Originally Posted by mp3qz

1./x,y,z>0 & x+y+z=3. Find Min:
$\frac{x^2}{x+2y^3}+\frac{y^2}{y+2z^3}+\frac{z^2}{z+2x^3}$

2./ x,y,z >0. Demonstrate:
$\frac{2\sqrt{x}}{x^3+y^2}+\frac{2\sqrt{y}}{y^3+z^2}+\frac{2\sqrt{z}}{z^3+x^2}\leq\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$

Hello : there is the solution from (2).
Look here

Rofl)

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