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5
Serbia national Olympiad Day 2 Problem 2
Serbia national Olympiad Day 2 Problem 2
Source: Serbia national Olympiad Day 2 Problem 2
March 28, 2015
Inequality
inequalities
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be nonnegative positive integers. Prove
x
−
y
x
y
+
2
y
+
1
+
y
−
z
z
y
+
2
z
+
1
+
z
−
x
x
z
+
2
x
+
1
≥
0
\frac{x-y}{xy+2y+1}+\frac{y-z}{zy+2z+1}+\frac{z-x}{xz+2x+1}\ge 0
x
y
+
2
y
+
1
x
−
y
+
zy
+
2
z
+
1
y
−
z
+
x
z
+
2
x
+
1
z
−
x
≥
0
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