if x = 9-4√5 then find x^3 -1/3x^3
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We have,
x=9−4
5
x
1
=9+4
5
Therefore,
x−
x
1
=−8
5
x+
x
1
=18
Since,
x
3
−
x
3
1
=(x−
x
1
)(x
2
+
x
2
1
+1)
=(−8
5
)
⎣
⎢
⎡
(x+
x
1
)
2
−1
⎦
⎥
⎤
=(−8
5
)[323]
=−2584
5
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