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1999 Tuymaada Olympiad
4
Tuymaada 1999, Q4
Tuymaada 1999, Q4
Source: Tuymaada 1999, Q4
July 31, 2012
inequalities
inequalities unsolved
Problem Statement
Prove the inequality
x
y
2
−
z
+
y
z
2
−
x
+
z
x
2
−
y
>
1
,
{x\over y^2-z}+{y\over z^2-x}+{z\over x^2-y} > 1,
y
2
−
z
x
+
z
2
−
x
y
+
x
2
−
y
z
>
1
,
where
2
<
x
,
y
,
z
<
4.
2 < x, y, z < 4.
2
<
x
,
y
,
z
<
4.
Proposed by A. Golovanov
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