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2023 NMTC Junior
P6
P6
Part of
2023 NMTC Junior
Problems
(1)
NMTC Junior 2023 P6
Source: NMTC Junior 2023 P6
11/8/2023
The sum of squares of four reals
x
,
y
,
z
,
u
x,y,z,u
x
,
y
,
z
,
u
is
1
1
1
. Find the minimum value of the expression
E
=
(
x
−
y
)
(
y
−
z
)
(
z
−
u
)
(
u
−
x
)
E=(x-y)(y-z)(z-u)(u-x)
E
=
(
x
−
y
)
(
y
−
z
)
(
z
−
u
)
(
u
−
x
)
. Find also the minimum values of
x
x
x
,
y
y
y
,
z
z
z
and
u
u
u
when this minimum occurs.
inequalities
nmtc