MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Japan MO Finals
2003 Japan MO Finals
3
find greatest number
find greatest number
Source: Japanese MO 2003, Problem 3
April 20, 2007
inequalities
inequalities unsolved
Problem Statement
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
)
.
Back to Problems
View on AoPS