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Iran MO (2nd Round)
1996 Iran MO (2nd round)
1
There exists a triangle [Iran Second Round 1996]
There exists a triangle [Iran Second Round 1996]
Source:
November 25, 2010
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be real numbers. Prove that there exists a triangle with side lengths
a
,
b
,
c
a, b, c
a
,
b
,
c
if and only if
2
(
a
4
+
b
4
+
c
4
)
<
(
a
2
+
b
2
+
c
2
)
2
.
2(a^4 + b^4 + c^4) < (a^2 + b^2 + c^2)^2.
2
(
a
4
+
b
4
+
c
4
)
<
(
a
2
+
b
2
+
c
2
)
2
.
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