MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran Team Selection Test
2015 Iran Team Selection Test
6
Inequality
Inequality
Source: Iran TST 2015, second exam, day 2, problem 3
May 17, 2015
inequalities
inequalities proposed
AM-GM
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers such that
a
+
b
+
c
=
a
b
c
a+b+c=abc
a
+
b
+
c
=
ab
c
prove that
a
b
c
3
2
(
∑
c
y
c
a
3
+
b
3
a
b
+
1
)
≥
∑
c
y
c
a
a
2
+
1
\frac{abc}{3\sqrt{2}}\left ( \sum_{cyc}\frac{\sqrt{a^3+b^3}}{ab+1} \right )\geq \sum_{cyc}\frac{a}{a^2+1}
3
2
ab
c
(
cyc
∑
ab
+
1
a
3
+
b
3
)
≥
cyc
∑
a
2
+
1
a
Back to Problems
View on AoPS