Estimate sqrt[3]{10} using newton method. Take x1 = 2 as initial guess.

Question

anonymous · Answer

It specifies to work with fractions, eg: x2 (which is really x1 if you consider initial to be xo) = ? / 6, x3 = ? / 1521

anonymous · Answer

Anyone?

campbell_st · Answer

so 

$$f(x) = x^3 - 10$$       f(2) = -2

$$f'(x) = 3x^2$$             f'(2) = 12

$$x _{1} = 2 - (-2)/12$$

$$x _{1} = 2 1/6$$

campbell_st · Answer

oops $$x _{1} = 13/6$$

anonymous · Answer

How do you even know to start with x^3 - 10? What's the math / algebra behind it, I'm curious.

anonymous · Answer

I've run into a problem for my second x, I end up with: x2 = (13/6) - (37/216) x (36/507). How do I simplify that? No matter how I try I end up getting 13/6 - (18.5/1521). Doesn't really make sense.