APMO 2004-5

Unread post by **SANZEED** » Fri Mar 09, 2012 9:55 pm

Prove that $(a^{2}+2)(b^{2}+2)(c^{2}+2)\ge 9(ab+bc+ca)$
for all positive real $a,b,c$.

zadid xcalibured · Unread post by **zadid xcalibured** » Sat Mar 10, 2012 3:05 pm

is it true that \[(abc)^2+2\geq ab+bc+ca\].

nafistiham · Unread post by **nafistiham** » Sat Mar 10, 2012 3:37 pm

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.

zadid xcalibured · Unread post by **zadid xcalibured** » Sat Mar 10, 2012 4:26 pm

a,b,c cant assume the value 0.

nafistiham · Unread post by **nafistiham** » Sat Mar 10, 2012 4:28 pm

zadid xcalibured wrote:a,b,c cant assume the value 0.

oops.didn`t see the word POSITIVE

Unread post by **Phlembac Adib Hasan** » Wed Mar 28, 2012 10:42 am

zadid xcalibured wrote:is it true that \[(abc)^2+2\geq ab+bc+ca\].

No.Take $a=10,b=\frac {1}{2},c=\frac {1}{5}$

Unread post by **SANZEED** » Sat May 26, 2012 7:54 pm

Will anyone post the reply,please ?

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