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South East Mathematical Olympiad
2019 South East Mathematical Olympiad
1
Non-homogeneous and asymmetric
Non-homogeneous and asymmetric
Source: 2019 CSMO Grade 10 P1
July 30, 2019
algebra
Inequality
China
Problem Statement
Find the largest real number
k
k
k
, such that for any positive real numbers
a
,
b
a,b
a
,
b
,
(
a
+
b
)
(
a
b
+
1
)
(
b
+
1
)
≥
k
a
b
2
(a+b)(ab+1)(b+1)\geq kab^2
(
a
+
b
)
(
ab
+
1
)
(
b
+
1
)
≥
ka
b
2
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