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National and Regional Contests
Germany Contests
German National Olympiad
2000 German National Olympiad
2
2
Part of
2000 German National Olympiad
Problems
(1)
min of f(x) = (x-1)^4 +(x-2)^4 +...+(x-n)^4
Source: Germany 2000 p2
2/23/2020
For an integer
n
≥
2
n \ge 2
n
≥
2
, find all real numbers
x
x
x
for which the polynomial
f
(
x
)
=
(
x
−
1
)
4
+
(
x
−
2
)
4
+
.
.
.
+
(
x
−
n
)
4
f(x) = (x-1)^4 +(x-2)^4 +...+(x-n)^4
f
(
x
)
=
(
x
−
1
)
4
+
(
x
−
2
)
4
+
...
+
(
x
−
n
)
4
takes its minimum value.
algebra
polynomial
min
inequalities