MathDB
Problems
Contests
International Contests
CentroAmerican
2012 CentroAmerican
3
Sum of 1/a+b = 1
Sum of 1/a+b = 1
Source: Centroamerican 2012, Problem 3
June 19, 2012
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be real numbers that satisfy
1
a
+
b
+
1
b
+
c
+
1
a
+
c
=
1
\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{a+c} =1
a
+
b
1
+
b
+
c
1
+
a
+
c
1
=
1
and
a
b
+
b
c
+
a
c
>
0
ab+bc+ac >0
ab
+
b
c
+
a
c
>
0
.Show that
a
+
b
+
c
−
a
b
c
a
b
+
b
c
+
a
c
≥
4
a+b+c - \frac{abc}{ab+bc+ac} \ge 4
a
+
b
+
c
−
ab
+
b
c
+
a
c
ab
c
≥
4
Back to Problems
View on AoPS