MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2016 India National Olympiad
P2
P2
Part of
2016 India National Olympiad
Problems
(1)
Which system of equalities implies $a=b=c$
Source: INMO 2016 Problem 2
1/17/2016
For positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
which of the following statements necessarily implies
a
=
b
=
c
a=b=c
a
=
b
=
c
: (I)
a
(
b
3
+
c
3
)
=
b
(
c
3
+
a
3
)
=
c
(
a
3
+
b
3
)
a(b^3+c^3)=b(c^3+a^3)=c(a^3+b^3)
a
(
b
3
+
c
3
)
=
b
(
c
3
+
a
3
)
=
c
(
a
3
+
b
3
)
, (II)
a
(
a
3
+
b
3
)
=
b
(
b
3
+
c
3
)
=
c
(
c
3
+
a
3
)
a(a^3+b^3)=b(b^3+c^3)=c(c^3+a^3)
a
(
a
3
+
b
3
)
=
b
(
b
3
+
c
3
)
=
c
(
c
3
+
a
3
)
? Justify your answer.
inequalities
inequalities proposed
algebra
algebra proposed