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Mathematics
Mathematics
Problem
If
x
=
5
−
21
2
x = \frac{5 - \sqrt{21}}{2}
x
=
2
5
−
21
then prove that
(
x
3
+
1
x
3
)
−
5
(
x
2
+
1
x
2
)
+
(
x
+
1
x
)
=
0
\left(x^3 + \frac{1}{x^3}\right) - 5\left(x^2 + \frac{1}{x^2}\right) + \left(x + \frac{1}{x}\right) = 0
(
x
3
+
x
3
1
)
−
5
(
x
2
+
x
2
1
)
+
(
x
+
x
1
)
=
0
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