if x-1/x=3+2root2 find the value of x cube - 1/xcube
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1
Answer:
It is given that,
x=2−
3
so,
1/x=1/(2−
3
)
By rationalizing the denominator, we get
=[1(2+
3
)]/[(2−
3
)(2+
3
)]
=[(2+
3
)]/[(2
2
)−(
3
)
2
]
=[(2+
3
)]/[4−3]
=2+
3
Now,
x−1/x=2−
3
−2−
3
=−2
3
Let us cube on both sides, we get
(x−1/x)
3
=(−2
3
)
3
x
3
−1/x
3
−3(x)(1/x)(x−1/x)=24
3
x
3
−1/x
3
−3(−2/
3
)=−24
3
x
3
−1/x
3
+6
3
=−24
3
x
3
−1/x
3
+6
3
=−24
3
x
3
−1/x
3
=−24
3
−6
3
=−30
3
Hence,
x
3
−1/x
3
=−30
3
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