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1970 IMO Longlists
44
(a+b)(b+c)(c+a) ≥ 8(a+b−c)(b+c−a)(c+a−b) (ILL 1970, P44)
(a+b)(b+c)(c+a) ≥ 8(a+b−c)(b+c−a)(c+a−b) (ILL 1970, P44)
Source: 0
May 22, 2011
inequalities
Problem Statement
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are side lengths of a triangle, prove that
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
8
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
.
(a + b)(b + c)(c + a) \geq 8(a + b - c)(b + c - a)(c + a - b).
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
8
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
.
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