Help me with this question please

Question

The number can be thought of as the solution of the equation .

Newton's method is an iterative numerical method to find roots (zeroes) of an equation of of the form . To implement Newton's method, one starts with an initial approximation and then computes a sequence of approximations via the formula , where .

To find , the iteration function is: .......................

Answer 1

x_n+1 = x_n - [x_n⁵ - 6]/5x_n⁴ = (4x_n⁵ + 6]/5x_n⁴

3/30/2022

I'm not sure what you tried to do, but here is what it should look like.

Start with x₁=2

x₂ = (4*32+6)/80 = 1.675

x₃ = (4*1.675⁵ + 6)/(5*1.675⁴) = 58.739262/39.357658 = 1..492448

The next iteration will be correct to at least 3 decimal places.