APMO 2004-5
Prove that $(a^{2}+2)(b^{2}+2)(c^{2}+2)\ge 9(ab+bc+ca)$
for all positive real $a,b,c$.
for all positive real $a,b,c$.
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- zadid xcalibured
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Re: APMO 2004-5
is it true that \[(abc)^2+2\geq ab+bc+ca\].
- nafistiham
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Re: APMO 2004-5
zadid xcalibured wrote:is it true that \[(abc)^2+2\geq ab+bc+ca\].
zadid, if any of $a,b,c$ is $0$ and the others are greater or equal than $2$ then it is not true.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
- zadid xcalibured
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Re: APMO 2004-5
a,b,c cant assume the value 0.
- nafistiham
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Re: APMO 2004-5
zadid xcalibured wrote:a,b,c cant assume the value 0.
oops.didn`t see the word POSITIVE
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
- Phlembac Adib Hasan
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Re: APMO 2004-5
No.Take $a=10,b=\frac {1}{2},c=\frac {1}{5}$zadid xcalibured wrote:is it true that \[(abc)^2+2\geq ab+bc+ca\].
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Re: APMO 2004-5
Will anyone post the reply,please ?
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