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I'm trying to determine if $$\bigl(x+y)^4(y+z)^4(z+x)^4 \geq$$ $$8x^2y^2z^2\bigl((x+y)^2 + (y+z)^2\bigr)\bigl((y+z)^2 + (z+x) ^2\bigr)\bigl((z+x)^2 + (x+y)^2\bigr)$$

for $x,y,z>0$.

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    I think Wolfram Alpha would help you much faster (if you ask nicely)!2012-08-06
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    The first part of your text read `{(x+y)(y+z)(z+x)}^4`: do you mean that **all** three terms are raised to the 4th power?2012-08-06
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    Fabian / Wolfram Alpha do times out. Enzotib / Yes $ (x+y)^4 (y+z)^4 (z+x)^4 $2012-08-06
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    Umm.. Would you let me know if you know a nice way to determine? Sine the homogeneousity of the expression, we can just set z=1 and then Mathematica show the graph is above the horizontal plane for x,y>0 but..2012-08-06
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    I edited my expression to be more clear.2012-08-06

3 Answers 3