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National and Regional Contests
Serbia Contests
Serbia Team Selection Test
2004 Serbia Team Selection Test
2
Serbia and Montenegro TST 2004
Serbia and Montenegro TST 2004
Source:
April 13, 2015
TST
inequalities
Serbia
three variable inequality
Problem Statement
Let
a
a
a
,
b
b
b
and
c
c
c
be real numbers such that
a
b
c
=
1
abc=1
ab
c
=
1
. Prove that the most two of numbers
2
a
−
1
b
,
2
b
−
1
c
,
2
c
−
1
a
2a-\frac{1}{b},\ 2b-\frac{1}{c},\ 2c-\frac{1}{a}
2
a
−
b
1
,
2
b
−
c
1
,
2
c
−
a
1
are greater than
1
1
1
.
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