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Problems
Contests
National and Regional Contests
Greece Contests
Greece JBMO TST
2008 Greece JBMO TST
2
2
Part of
2008 Greece JBMO TST
Problems
(1)
(a^2b^2)/(a+b)+(b^2c^2)/(b+c)+(c^2a^2)/(c+a) <=(a^3+b^3+c^3)/2
Source: Greece JBMO TST 2008 p2
4/29/2019
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers, prove that
a
2
b
2
a
+
b
+
b
2
c
2
b
+
c
+
c
2
a
2
c
+
a
≤
a
3
+
b
3
+
c
3
2
\frac{a^2b^2}{a+b}+\frac{b^2c^2}{b+c}+\frac{c^2a^2}{c+a}\le \frac{a^3+b^3+c^3}{2}
a
+
b
a
2
b
2
+
b
+
c
b
2
c
2
+
c
+
a
c
2
a
2
≤
2
a
3
+
b
3
+
c
3
algebra
inequalities
three variable inequality