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A
Simple Inequality
Simple Inequality
Source:
December 22, 2021
Inequality
AM-GM
math
simple
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
a
b
c
=
1
abc = 1
ab
c
=
1
. Prove that
(
a
+
b
+
c
)
(
a
b
+
b
c
+
c
a
)
+
3
≥
4
(
a
+
b
+
c
)
.
(a + b + c)(ab + bc + ca) + 3\ge 4(a + b + c).
(
a
+
b
+
c
)
(
ab
+
b
c
+
c
a
)
+
3
≥
4
(
a
+
b
+
c
)
.
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