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2019 Turkey Junior National Olympiad
2
Inequality about x^5+y^5+z^5
Inequality about x^5+y^5+z^5
Source: Turkey Junior Math Olympiad 2019 #2
December 23, 2019
inequalities
inequalities proposed
Problem Statement
x
,
y
,
z
∈
R
+
x,y,z \in \mathbb{R}^+
x
,
y
,
z
∈
R
+
and
x
5
+
y
5
+
z
5
=
x
y
+
y
z
+
z
x
x^5+y^5+z^5=xy+yz+zx
x
5
+
y
5
+
z
5
=
x
y
+
yz
+
z
x
. Prove that
3
≥
x
2
y
+
y
2
z
+
z
2
x
3 \ge x^2y+y^2z+z^2x
3
≥
x
2
y
+
y
2
z
+
z
2
x
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