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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
10.6
a^3 - a- 1 = 0 - VI Soros Olympiad 1999-00 Round 1 10.6
a^3 - a- 1 = 0 - VI Soros Olympiad 1999-00 Round 1 10.6
Source:
May 21, 2024
algebra
Problem Statement
Let
a
3
−
a
−
1
=
0
a^3 - a- 1 = 0
a
3
−
a
−
1
=
0
. Find the exact value of the expression
3
a
2
−
4
a
3
+
a
2
a
2
+
3
a
+
2
4
.
\sqrt[3]{3a^2-4a} + a\sqrt[4]{2a^2+3a+2}.
3
3
a
2
−
4
a
+
a
4
2
a
2
+
3
a
+
2
.
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