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Kürschák Math Competition
1972 Kurschak Competition
1
1
Part of
1972 Kurschak Competition
Problems
(1)
a(b -c)^2 + b(c - a)^2 + c(a - b)^2 + 4abc > a^3 + b^3 + c^3
Source: 1972 Hungary - Kürschák Competition p1
10/15/2022
A triangle has side lengths
a
,
b
,
c
a, b, c
a
,
b
,
c
. Prove that
a
(
b
−
c
)
2
+
b
(
c
−
a
)
2
+
c
(
a
−
b
)
2
+
4
a
b
c
>
a
3
+
b
3
+
c
3
a(b -c)^2 + b(c - a)^2 + c(a - b)^2 + 4abc > a^3 + b^3 + c^3
a
(
b
−
c
)
2
+
b
(
c
−
a
)
2
+
c
(
a
−
b
)
2
+
4
ab
c
>
a
3
+
b
3
+
c
3
geometry
Geometric Inequalities
inequalities