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Baltic Way
2013 Baltic Way
4
4
Part of
2013 Baltic Way
Problems
(1)
Inequality
Source: 2013 Baltic Way, Problem 4
12/30/2013
Prove that the following inequality holds for all positive real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
:
x
3
y
2
+
z
2
+
y
3
z
2
+
x
2
+
z
3
x
2
+
y
2
≥
x
+
y
+
z
2
.
\dfrac{x^3}{y^2+z^2}+\dfrac{y^3}{z^2+x^2}+\dfrac{z^3}{x^2+y^2}\ge \dfrac{x+y+z}{2}.
y
2
+
z
2
x
3
+
z
2
+
x
2
y
3
+
x
2
+
y
2
z
3
≥
2
x
+
y
+
z
.
inequalities
function
rearrangement inequality
inequalities unsolved