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Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
9.8
f(\sqrt[3]{2}-1) (V Soros Olympiad 1998-99 Round 3 9.8)
f(\sqrt[3]{2}-1) (V Soros Olympiad 1998-99 Round 3 9.8)
Source:
May 25, 2024
algebra
polynomial
Problem Statement
Calculate
f
(
2
3
−
1
)
f(\sqrt[3]{2}-1)
f
(
3
2
−
1
)
, where
f
(
x
)
=
x
1999
+
3
x
1998
+
4
x
1997
+
2
x
1996
+
4
x
1995
+
2
x
1994
+
.
.
.
f(x) = x^{1999} + 3x^{1998} + 4x^{1997} + 2x^{1996} + 4x^{1995} + 2x^{1994} + ...
f
(
x
)
=
x
1999
+
3
x
1998
+
4
x
1997
+
2
x
1996
+
4
x
1995
+
2
x
1994
+
...
.
.
.
+
4
x
3
+
2
x
2
+
3
x
+
1.
... + 4x^3 + 2x^2 + 3x+ 1.
...
+
4
x
3
+
2
x
2
+
3
x
+
1.
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