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Balkan MO Shortlist
2016 Balkan MO Shortlist
A1
A1
Part of
2016 Balkan MO Shortlist
Problems
(1)
\sqrt{a^3b+a^3c}+\sqrt{b^3c+b^3a}+\sqrt{c^3a+c^3b}\ge 4/3 (ab+bc+ca)
Source: Balkan BMO Shortlist 2016 A1
7/30/2019
Let
a
,
b
,
c
a, b,c
a
,
b
,
c
be positive real numbers. Prove that
a
3
b
+
a
3
c
+
b
3
c
+
b
3
a
+
c
3
a
+
c
3
b
≥
4
3
(
a
b
+
b
c
+
c
a
)
\sqrt{a^3b+a^3c}+\sqrt{b^3c+b^3a}+\sqrt{c^3a+c^3b}\ge \frac43 (ab+bc+ca)
a
3
b
+
a
3
c
+
b
3
c
+
b
3
a
+
c
3
a
+
c
3
b
≥
3
4
(
ab
+
b
c
+
c
a
)
inequalities
three variable inequality
algebra
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