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International Contests
APMO
2022 APMO
5
5
Part of
2022 APMO
Problems
(1)
Inequality on APMO P5
Source: APMO 2022 P5
5/17/2022
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be real numbers such that
a
2
+
b
2
+
c
2
+
d
2
=
1
a^2+b^2+c^2+d^2=1
a
2
+
b
2
+
c
2
+
d
2
=
1
. Determine the minimum value of
(
a
−
b
)
(
b
−
c
)
(
c
−
d
)
(
d
−
a
)
(a-b)(b-c)(c-d)(d-a)
(
a
−
b
)
(
b
−
c
)
(
c
−
d
)
(
d
−
a
)
and determine all values of
(
a
,
b
,
c
,
d
)
(a,b,c,d)
(
a
,
b
,
c
,
d
)
such that the minimum value is achived.
inequalities
APMO
APMO 2022