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Polish MO Finals
1951 Polish MO Finals
3
ab (a + b) + bc (b + c) + ca (c + a) >= 6abc.
ab (a + b) + bc (b + c) + ca (c + a) >= 6abc.
Source: Polish MO Finals 1951 p 2
August 28, 2024
algebra
inequalities
Problem Statement
Prove that if
a
>
0
a > 0
a
>
0
,
b
>
0
b > 0
b
>
0
,
c
>
0
c > 0
c
>
0
, then the inequality holds
a
b
(
a
+
b
)
+
b
c
(
b
+
c
)
+
c
a
(
c
+
a
)
≥
6
a
b
c
.
ab (a + b) + bc (b + c) + ca (c + a) \geq 6abc.
ab
(
a
+
b
)
+
b
c
(
b
+
c
)
+
c
a
(
c
+
a
)
≥
6
ab
c
.
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