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India IMO Training Camp
2014 India IMO Training Camp
2
Eighth power inequality
Eighth power inequality
Source: IMOTC 2014 Practice Test 1 Problem 2
July 11, 2014
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
a,b
a
,
b
be positive real numbers.Prove that
(
1
+
a
)
8
+
(
1
+
b
)
8
≥
128
a
b
(
a
+
b
)
2
(1+a)^{8}+(1+b)^{8}\geq 128ab(a+b)^{2}
(
1
+
a
)
8
+
(
1
+
b
)
8
≥
128
ab
(
a
+
b
)
2
.
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