MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
2011 Greece Junior Math Olympiad
4
Inequality
Inequality
Source: Archimedes Junior 2011
March 17, 2020
inequalities
Problem Statement
If
x
,
y
,
z
x, y, z
x
,
y
,
z
are positive real numbers with sum
12
12
12
, prove that
x
y
+
y
z
+
z
x
+
3
≥
x
+
y
+
z
\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+ 3 \ge \sqrt{x} +\sqrt{y }+\sqrt{z}
y
x
+
z
y
+
x
z
+
3
≥
x
+
y
+
z
. When equality is valid?
Back to Problems
View on AoPS