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South East Mathematical Olympiad
2023 South East Mathematical Olympiad
1
Easy 2-variable inequality
Easy 2-variable inequality
Source: China Southeast MO 2023 Grade11 Day1 Problem1
July 30, 2023
inequalities
Problem Statement
Let
a
,
b
>
0
a, b>0
a
,
b
>
0
. Prove that:
(
a
3
+
b
3
+
a
3
b
3
)
(
1
a
3
+
1
b
3
+
1
a
3
b
3
)
+
27
≥
6
(
a
+
b
+
1
a
+
1
b
+
a
b
+
b
a
)
(a^3+b^3+a^3b^3)(\frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{a^3b^3} ) +27 \ge 6(a+b+\frac{1}{a} +\frac{1}{b} +\frac{a}{b} +\frac{b}{a})
(
a
3
+
b
3
+
a
3
b
3
)
(
a
3
1
+
b
3
1
+
a
3
b
3
1
)
+
27
≥
6
(
a
+
b
+
a
1
+
b
1
+
b
a
+
a
b
)
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