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$x_{1}^{2}+x_{2}^{2}+...+x_{n}^{2}\leq -n.m.M$


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#1
iloveyou123

iloveyou123

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1) Cho $x_{1},x_{2},...x_{n}$ là các số thoả mãn $x_{1}+x_{2},...+x_{n}=0$
gọi m=min {$x_{i}$} và M=max{$x_{i}$}
cmr $x_{1}^{2}+x_{2}^{2}+...+x_{n}^{2}\leq -n.m.M$
2) Cho $x_{1},x_{2},...x_{n}$ >0
gọi m=min{$x_{i}$} và M=max{$x_{i}$}
cmr $n^{2}\leq (x_{1}+x_{2}+..+x_{n})(\frac{1}{x_{1}}+\frac{1}{x_{2}}+...+\frac{1}{x_{n}})\leq n^{2}.\frac{(m+M)^{2}}{4mM}$

Edited by iloveyou123, 02-11-2012 - 11:31.





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