MathDB
Problems
Contests
International Contests
IMO Longlists
1990 IMO Longlists
5
Fractional Inequality - ILL 1990 VIE2
Fractional Inequality - ILL 1990 VIE2
Source:
September 19, 2010
inequalities
inequalities proposed
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive reals and
x
≥
y
≥
z
x \geq y \geq z
x
≥
y
≥
z
. Prove that
x
2
y
z
+
y
2
z
x
+
z
2
x
y
≥
x
2
+
y
2
+
z
2
\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{z^2x}{y} \geq x^2+y^2+z^2
z
x
2
y
+
x
y
2
z
+
y
z
2
x
≥
x
2
+
y
2
+
z
2
Back to Problems
View on AoPS