MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
2017 Turkey Team Selection Test
5
Turkey TST 2017 P5
Turkey TST 2017 P5
Source: Turkey TST 2017 P5
June 1, 2017
Turkey
TST
algebra
inequalities
Problem Statement
For all positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
, show that
a
3
b
+
b
3
c
+
c
3
a
+
9
≥
4
(
a
b
+
b
c
+
c
a
)
.
a^3b+b^3c+c^3a+9\geq 4(ab+bc+ca).
a
3
b
+
b
3
c
+
c
3
a
+
9
≥
4
(
ab
+
b
c
+
c
a
)
.
Back to Problems
View on AoPS