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National and Regional Contests
Moldova Contests
Chisinau City MO
1975 Chisinau City MO
117
117
Part of
1975 Chisinau City MO
Problems
(1)
Chisinau MO p117 1975 R2 X tan^2 80^o root of x^3 - 33x^2 + 27x - 33 = 0
Source:
3/16/2021
Prove that the numbers
tan
2
2
0
o
,
tan
2
4
0
o
,
tan
2
8
0
o
\tan^2 20^o, \tan^2 40^o,\tan^2 80^o
tan
2
2
0
o
,
tan
2
4
0
o
,
tan
2
8
0
o
are the roots of the equation
x
3
−
33
x
2
+
27
x
−
33
=
0
x^3 - 33x^2 + 27x - 33 = 0
x
3
−
33
x
2
+
27
x
−
33
=
0
.
trigonometry
Cubic