in Newtowrite the formula for finding cuben rapshson method root of the number n
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Answer
Let x=
3
N
⟹x
3
=N
⟹x
3
−N=0.
Newton-Raphson method ⇒ x
n+1
=x
n
−
f
′
(x
n
)
f(x
n
)
f(x)=x
3
−N
f
′
(x)=3x
2
∴ x
n+1
=x
n
−
3x
n
2
x
n
3
−N
x
n+1
=x
n
−
3x
n
2
x
n
3
+
3x
n
2
N
x
n+1
=x
n
−
3
x
n
+
3x
n
2
N
x
n+1
=
3
2x
n
+
3x
n
2
N
x
n+1
=
3
1
[2x
n
+
x
n
2
N
]
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