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2014 Baltic Way
3
Inequality, Baltic Way 2014, Problem 3
Inequality, Baltic Way 2014, Problem 3
Source:
November 11, 2014
inequalities
Baltic Way
Problem Statement
Positive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
1
a
+
1
b
+
1
c
=
3.
\frac{1}{a} +\frac{1}{b} +\frac{1}{c} = 3.
a
1
+
b
1
+
c
1
=
3.
Prove the inequality
1
a
3
+
b
+
1
b
3
+
c
+
1
c
3
+
a
≤
3
2
.
\frac{1}{\sqrt{a^3+ b}}+\frac{1}{\sqrt{b^3 + c}}+\frac{1}{\sqrt{c^3 + a}}\leq \frac{3}{\sqrt{2}}.
a
3
+
b
1
+
b
3
+
c
1
+
c
3
+
a
1
≤
2
3
.
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