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Turkey MO (2nd round)
2019 Turkey MO (2nd round)
1
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Part of
2019 Turkey MO (2nd round)
Problems
(1)
inequality, p1
Source: Turkey National Mathematical Olympiad 2019 P1
12/22/2019
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive real numbers such that
(
a
b
−
1
)
(
b
c
−
1
)
(
c
a
−
1
)
=
1
(\sqrt {ab}-1)(\sqrt {bc}-1)(\sqrt {ca}-1)=1
(
ab
−
1
)
(
b
c
−
1
)
(
c
a
−
1
)
=
1
At most, how many of the numbers:
a
−
b
c
,
a
−
c
b
,
b
−
a
c
,
b
−
c
a
,
c
−
a
b
,
c
−
b
a
a-\frac {b}{c}, a-\frac {c}{b}, b-\frac {a}{c}, b-\frac {c}{a}, c-\frac {a}{b}, c-\frac {b}{a}
a
−
c
b
,
a
−
b
c
,
b
−
c
a
,
b
−
a
c
,
c
−
b
a
,
c
−
a
b
can be bigger than
1
1
1
?
inequalities
turkey MO 2019 p1