MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2018 Hanoi Open Mathematics Competitions
14
max T= (a-b)^{2018}+(b-c)^{2018}+(c-a)^{2018} (HOMC 2018 ind. sen14)
max T= (a-b)^{2018}+(b-c)^{2018}+(c-a)^{2018} (HOMC 2018 ind. sen14)
Source:
February 2, 2020
maximum
inequalities
algebra
Problem Statement
Let
a
,
b
,
c
a,b, c
a
,
b
,
c
denote the real numbers such that
1
≤
a
,
b
,
c
≤
2
1 \le a, b, c\le 2
1
≤
a
,
b
,
c
≤
2
. Consider
T
=
(
a
−
b
)
2018
+
(
b
−
c
)
2018
+
(
c
−
a
)
2018
T = (a - b)^{2018} + (b - c)^{2018} + (c - a)^{2018}
T
=
(
a
−
b
)
2018
+
(
b
−
c
)
2018
+
(
c
−
a
)
2018
. Determine the largest possible value of
T
T
T
.
Back to Problems
View on AoPS