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a^3+b^3+c^3+2[(ab)^3+(bc)^3+(ca)^3] >= 3(a^2b+b^2c+c^2a) (HOMCJ'15-9)
a^3+b^3+c^3+2[(ab)^3+(bc)^3+(ca)^3] >= 3(a^2b+b^2c+c^2a) (HOMCJ'15-9)
Source:
August 6, 2019
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b,c
a
,
b
,
c
be positive numbers with
a
b
c
=
1
abc = 1
ab
c
=
1
. Prove that
a
3
+
b
3
+
c
3
+
2
[
(
a
b
)
3
+
(
b
c
)
3
+
(
c
a
)
3
]
≥
3
(
a
2
b
+
b
2
c
+
c
2
a
)
a^3 + b^3 + c^3 + 2[(ab)^3 + (bc)^3 + (ca)^3] \ge 3(a^2b + b^2c + c^2a)
a
3
+
b
3
+
c
3
+
2
[(
ab
)
3
+
(
b
c
)
3
+
(
c
a
)
3
]
≥
3
(
a
2
b
+
b
2
c
+
c
2
a
)
.
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