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2013 Indonesia MO
3
3
Part of
2013 Indonesia MO
Problems
(1)
Find M so one number exceeds the target
Source: Indonesian Mathematical Olympiad 2013 Problem 3
9/5/2013
Determine all positive real
M
M
M
such that for any positive reals
a
,
b
,
c
a,b,c
a
,
b
,
c
, at least one of
a
+
M
a
b
,
b
+
M
b
c
,
c
+
M
c
a
a + \dfrac{M}{ab}, b + \dfrac{M}{bc}, c + \dfrac{M}{ca}
a
+
ab
M
,
b
+
b
c
M
,
c
+
c
a
M
is greater than or equal to
1
+
M
1+M
1
+
M
.
inequalities
inequalities unsolved