MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Soros Olympiad in Mathematics
I Soros Olympiad 1994-95 (Rus + Ukr)
9.9
sum a/(b^2-1)>=2 for a,b,c>1, a+b+c= 6 (I Soros Olympiad 1994-95 R1 9.9)
sum a/(b^2-1)>=2 for a,b,c>1, a+b+c= 6 (I Soros Olympiad 1994-95 R1 9.9)
Source:
July 31, 2021
algebra
inequalities
Problem Statement
Given the following real numbers
a
.
b
,
c
a. b, c
a
.
b
,
c
greater than one that
a
+
b
+
c
=
6
a + b + c = 6
a
+
b
+
c
=
6
. Prove the inequality
a
b
2
−
1
+
b
c
2
−
1
+
c
a
2
−
1
≥
2
\frac{a}{b^2-1}+\frac{b}{c^2-1}+\frac{c}{a^2-1}\ge 2
b
2
−
1
a
+
c
2
−
1
b
+
a
2
−
1
c
≥
2
Back to Problems
View on AoPS