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$$J\leqq xz\left( xy+ zx+ 2y^{2} \right )$$

inequality

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DOTOANNANG

DOTOANNANG

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  • ĐHV Toán Cao cấp
  • 1609 posts

$x,\,y,\,z\geqq 0$. Chứng minh rằng:

 

$$J= \frac{9}{8}\,y^{2}\left ( 2x-y \right )^{2}+ \frac{1}{16}\left ( 2x-y \right )^{4}+ \frac{1}{2}\,y\left ( 2x-y \right )^{3}+ \frac{1}{16}\left ( 16y^{3}z- 59y^{4} \right )\leqq xz\left( xy+ zx+ 2y^{2} \right )$$







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