MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1996 All-Russian Olympiad Regional Round
10.1
a+b+c > 3 if ab + bc + ca > a+ b + c - All-Russian MO 1996 Regional (R4) 10.1
a+b+c > 3 if ab + bc + ca > a+ b + c - All-Russian MO 1996 Regional (R4) 10.1
Source:
September 23, 2024
algebra
inequalities
Problem Statement
Prove that if
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive numbers and
a
b
+
b
c
+
c
a
>
a
+
b
+
c
ab + bc + ca > a+ b + c
ab
+
b
c
+
c
a
>
a
+
b
+
c
, then
a
+
b
+
c
>
3
a + b + c > 3
a
+
b
+
c
>
3
.
Back to Problems
View on AoPS