MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CHMMC problems
2021 CHMMC Winter (2021-22)
1
CHMMC 2021-22 Proof 1 (a-b)(b-c) + (b-c)(c-a) + (c-a)(a-b) = 0
CHMMC 2021-22 Proof 1 (a-b)(b-c) + (b-c)(c-a) + (c-a)(a-b) = 0
Source:
September 1, 2022
algebra
Problem Statement
Find all ordered triples
(
a
,
b
,
c
)
(a,b, c)
(
a
,
b
,
c
)
of real numbers such that
(
a
−
b
)
(
b
−
c
)
+
(
b
−
c
)
(
c
−
a
)
+
(
c
−
a
)
(
a
−
b
)
=
0.
(a-b)(b-c) + (b-c)(c-a) + (c-a)(a-b) = 0.
(
a
−
b
)
(
b
−
c
)
+
(
b
−
c
)
(
c
−
a
)
+
(
c
−
a
)
(
a
−
b
)
=
0.
Back to Problems
View on AoPS