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5
1/(a^3 + 3b)+1/(b^3 + 3a)<=1/2 OLCOMA Costa Rica 2015 p5 day2
1/(a^3 + 3b)+1/(b^3 + 3a)<=1/2 OLCOMA Costa Rica 2015 p5 day2
Source:
September 30, 2021
algebra
inequalities
Problem Statement
Let
a
,
b
∈
R
+
a,b \in R^+
a
,
b
∈
R
+
with
a
b
=
1
ab = 1
ab
=
1
, prove that
1
a
3
+
3
b
+
1
b
3
+
3
a
≤
1
2
.
\frac{1}{a^3 + 3b}+\frac{1}{b^3 + 3a}\le \frac12.
a
3
+
3
b
1
+
b
3
+
3
a
1
≤
2
1
.
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