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Poland - Second Round
1979 Poland - Second Round
2
a^3 + b^3 + c^3 + 3abc \geq a^2(b + c) + b^2(a + c) + c^2(a + b)
a^3 + b^3 + c^3 + 3abc \geq a^2(b + c) + b^2(a + c) + c^2(a + b)
Source: Polish MO Recond Round 1979 p2
September 9, 2024
algebra
inequalities
Problem Statement
Prove that if
a
,
b
,
c
a, b, c
a
,
b
,
c
are non-negative numbers, then
a
3
+
b
3
+
c
3
+
3
a
b
c
≥
a
2
(
b
+
c
)
+
b
2
(
a
+
c
)
+
c
2
(
a
+
b
)
.
a^3 + b^3 + c^3 + 3abc \geq a^2(b + c) + b^2(a + c) + c^2(a + b).
a
3
+
b
3
+
c
3
+
3
ab
c
≥
a
2
(
b
+
c
)
+
b
2
(
a
+
c
)
+
c
2
(
a
+
b
)
.
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