MathDB
Problems
Contests
International Contests
Junior Balkan MO
2003 Junior Balkan MO
4
x,y,z
x,y,z
Source: 7th JBMO 2003, Problem 4
June 11, 2004
inequalities
High School Olympiads
algebra
JBMO
Problem Statement
Let
x
,
y
,
z
>
−
1
x, y, z > -1
x
,
y
,
z
>
−
1
. Prove that
1
+
x
2
1
+
y
+
z
2
+
1
+
y
2
1
+
z
+
x
2
+
1
+
z
2
1
+
x
+
y
2
≥
2.
\frac{1+x^2}{1+y+z^2} + \frac{1+y^2}{1+z+x^2} + \frac{1+z^2}{1+x+y^2} \geq 2.
1
+
y
+
z
2
1
+
x
2
+
1
+
z
+
x
2
1
+
y
2
+
1
+
x
+
y
2
1
+
z
2
≥
2.
Laurentiu Panaitopol
Back to Problems
View on AoPS