MathDB
Problems
Contests
National and Regional Contests
Italy Contests
ITAMO
1990 ITAMO
4
4
Part of
1990 ITAMO
Problems
(1)
a^2+b^2+c^2 +4abc<= \frac12, for sidelengths with a+b+c=1 (likely classic)
Source: 1990 ITAMO p4
1/31/2020
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be side lengths of a triangle with
a
+
b
+
c
=
1
a+b+c = 1
a
+
b
+
c
=
1
. Prove that
a
2
+
b
2
+
c
2
+
4
a
b
c
≤
1
2
a^2 +b^2 +c^2 +4abc \le \frac12
a
2
+
b
2
+
c
2
+
4
ab
c
≤
2
1
.
inequalities
algebra
geometric inequality