MathDB
Problems
Contests
International Contests
Tuymaada Olympiad
2005 Tuymaada Olympiad
8
8
Part of
2005 Tuymaada Olympiad
Problems
(1)
sum of squares = 1 kind of ineq
Source: Tuymaada, Day 2, Problem 8
7/30/2005
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive reals s.t.
a
2
+
b
2
+
c
2
=
1
a^2+b^2+c^2=1
a
2
+
b
2
+
c
2
=
1
. Prove the following inequality
∑
a
a
3
+
b
c
>
3.
\sum \frac{a}{a^3+bc} >3 .
∑
a
3
+
b
c
a
>
3.
Proposed by A. Khrabrov
inequalities
inequalities proposed