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Contests
National and Regional Contests
Italy Contests
ITAMO
1992 ITAMO
5
Inequality
Inequality
Source:
July 15, 2016
inequalities
Problem Statement
a
a
a
,
b
b
b
,
c
c
c
are real numbers. Show that
min
(
(
a
−
b
)
2
,
(
b
−
c
)
2
,
(
c
−
a
)
2
)
≤
a
2
+
b
2
+
c
2
2
\min((a-b)^2,(b-c)^2,(c-a)^2)\leq \frac{a^2+b^2+c^2}{2}
min
((
a
−
b
)
2
,
(
b
−
c
)
2
,
(
c
−
a
)
2
)
≤
2
a
2
+
b
2
+
c
2
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