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I am asked to find $\sqrt{2012}$ using Newton-Raphson's Method with the following recursive method

$x_{n+1} = \frac{1}{2} (x_n + \frac{a}{x_n}) $

I notied that give same answers as using

x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

This is easy, but the next part asks to find a similar recursive method to find $\sqrt[3]{2012}$. How do I find such a method?

UPDATE

I did

x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 12.7551

$x_2 = 12.6257$

$x_3 = 12.6244$

$x_4 = 12.6244$

$x_4 ^ 3 = 2012.02$

Which seems correct. But I didn't use a similar recursive method like the question asked?

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    If you use the idea described by Robert Israel, and fool around with the resulting formula$a$bit, you will end up with something that has a shape very similar to the one for square root.2012-03-14

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Hint: What does Newton's method say for $f(x) = x^3 - a$?