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IFYM Int. Fest. of Young Mathematicians, Sozopol
2010 IFYM, Sozopol
2
Find the biggest value
Find the biggest value
Source:
July 18, 2011
inequalities
inequalities unsolved
Problem Statement
If
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
and
a
b
c
=
3
abc=3
ab
c
=
3
,find the biggest value of:
a
2
b
2
a
7
+
a
3
b
3
c
+
b
7
+
b
2
c
2
b
7
+
b
3
c
3
a
+
c
7
+
c
2
a
2
c
7
+
c
3
a
3
b
+
a
7
\frac{a^2b^2}{a^7+a^3b^3c+b^7}+\frac{b^2c^2}{b^7+b^3c^3a+c^7}+\frac{c^2a^2}{c^7+c^3a^3b+a^7}
a
7
+
a
3
b
3
c
+
b
7
a
2
b
2
+
b
7
+
b
3
c
3
a
+
c
7
b
2
c
2
+
c
7
+
c
3
a
3
b
+
a
7
c
2
a
2
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