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Japan MO Finals
2003 Japan MO Finals
3
3
Part of
2003 Japan MO Finals
Problems
(1)
find greatest number
Source: Japanese MO 2003, Problem 3
4/20/2007
Find the greatest real number
k
k
k
such that, for any positive
a
,
b
,
c
a,b,c
a
,
b
,
c
with
a
2
>
b
c
a^{2}>bc
a
2
>
b
c
,
(
a
2
−
b
c
)
2
>
k
(
b
2
−
c
a
)
(
c
2
−
a
b
)
(a^{2}-bc)^{2}>k(b^{2}-ca)(c^{2}-ab)
(
a
2
−
b
c
)
2
>
k
(
b
2
−
c
a
)
(
c
2
−
ab
)
.
inequalities
inequalities unsolved