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2021 Iran MO (2nd Round)
5
5
Part of
2021 Iran MO (2nd Round)
Problems
(1)
Three numbers among 1400 given numbers have certain property
Source: 2021 Iran second round mathematical Olympiad P5
5/16/2021
1400 real numbers are given. Prove that one can choose three of them like
x
,
y
,
z
x,y,z
x
,
y
,
z
such that :
∣
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
x
4
+
y
4
+
z
4
+
1
∣
<
0.009
\left|\frac{(x-y)(y-z)(z-x)}{x^4+y^4+z^4+1}\right| < 0.009
x
4
+
y
4
+
z
4
+
1
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
<
0.009
combinatorics
algebra
inequalities
Iran