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IMO Longlists
1986 IMO Longlists
60
Three variables inequality
Three variables inequality
Source:
August 29, 2010
inequalities
geometry
perimeter
inequalities proposed
Problem Statement
Prove the inequality
(
−
a
+
b
+
c
)
2
(
a
−
b
+
c
)
2
(
a
+
b
−
c
)
2
≥
(
−
a
2
+
b
2
+
c
2
)
(
a
2
−
b
2
+
c
2
)
(
a
2
+
b
2
−
c
2
)
(-a+b+c)^2(a-b+c)^2(a+b-c)^2 \geq (-a^2+b^2+c^2)(a^2-b^2+c^2)(a^2+b^2-c^2)
(
−
a
+
b
+
c
)
2
(
a
−
b
+
c
)
2
(
a
+
b
−
c
)
2
≥
(
−
a
2
+
b
2
+
c
2
)
(
a
2
−
b
2
+
c
2
)
(
a
2
+
b
2
−
c
2
)
for all real numbers
a
,
b
,
c
.
a, b, c.
a
,
b
,
c
.
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