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Romania - Local Contests
Nicolae Coculescu
2007 Nicolae Coculescu
4
Shur-like inequality
Shur-like inequality
Source:
December 13, 2019
inequalities
Problem Statement
Let be three nonnegative integers
m
,
n
,
p
m,n,p
m
,
n
,
p
and three real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
such that
2
m
x
+
2
n
y
+
2
p
z
≥
0.
2^mx+2^ny+2^pz\ge 0.
2
m
x
+
2
n
y
+
2
p
z
≥
0.
Prove:
2
m
(
2
x
−
1
)
+
2
n
(
2
y
−
1
)
+
2
p
(
2
z
−
1
)
≥
0
2^m\left( 2^x-1 \right)+2^n\left( 2^y-1 \right)+2^p\left( 2^z-1 \right)\ge 0
2
m
(
2
x
−
1
)
+
2
n
(
2
y
−
1
)
+
2
p
(
2
z
−
1
)
≥
0
Cristinel Mortici
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