If x-2/x=3,then x^3-8/x^3=
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Step-by-step explanation:
Given ⇒ x−
x
2
=3…(i)
We have to find x
3
−
x
3
8
Cube on both side of (i),
(x−
x
2
)
3
=(3)
3
⇒x
3
−
x
3
2
3
−3⋅x⋅(
x
2
)(x−
x
2
)=27 by using (a−b)
3
=a
3
−b
3
−3ab(a−b)
⇒x
3
−
x
3
8
−6(3)=27
⇒x
3
−
x
3
8
=27+18
⇒x
3
−
x
3
8
=45
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