MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1997 India National Olympiad
3
Simple one!
Simple one!
Source: INMO 1997 Problem 3
October 6, 2005
inequalities
function
algebra unsolved
algebra
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are three real numbers and
a
+
1
b
=
b
+
1
c
=
c
+
1
a
=
t
a + \dfrac{1}{b} = b + \dfrac{1}{c} = c + \dfrac{1}{a} = t
a
+
b
1
=
b
+
c
1
=
c
+
a
1
=
t
for some real number
t
t
t
, prove that
a
b
c
+
t
=
0.
abc + t = 0 .
ab
c
+
t
=
0.
Back to Problems
View on AoPS