MathDB
Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
1995 India Regional Mathematical Olympiad
5
A triangle ineq - well known
A triangle ineq - well known
Source: Indian RMO 1995 Problem 5
October 26, 2005
inequalities
quadratics
Problem Statement
Show that for any triangle
A
B
C
ABC
A
BC
, the following inequality is true:
a
2
+
b
2
+
c
2
>
3
m
a
x
{
∣
a
2
−
b
2
∣
,
∣
b
2
−
c
2
∣
,
∣
c
2
−
a
2
∣
}
.
a^2 + b^2 +c^2 > \sqrt{3} max \{ |a^2 - b^2|, |b^2 -c^2|, |c^2 -a^2| \} .
a
2
+
b
2
+
c
2
>
3
ma
x
{
∣
a
2
−
b
2
∣
,
∣
b
2
−
c
2
∣
,
∣
c
2
−
a
2
∣
}
.
Back to Problems
View on AoPS