MathDB
Problems
Contests
National and Regional Contests
Bulgaria Contests
Bulgaria JBMO Team Selection Test
2014 Bulgaria JBMO TST
2
2
Part of
2014 Bulgaria JBMO TST
Problems
(1)
Maximum of a+b+c
Source:
5/18/2015
Find the maximum possible value of
a
+
b
+
c
,
a + b + c ,
a
+
b
+
c
,
if
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers such that
a
2
+
b
2
+
c
2
=
a
3
+
b
3
+
c
3
.
a^2 + b^2 + c^2 = a^3 + b^3 + c^3 .
a
2
+
b
2
+
c
2
=
a
3
+
b
3
+
c
3
.
inequalities