Use Newton's method to approximate a root of the equation

Question

Use Newton's method to approximate a root of the equation ³ as follows.

Let ₁ be the initial approximation.

The second approximation ₂ is 

the third approximation ₃ is.

(Although these are approximations of the root, enter exact expressions for each approximation.)

Answer 1

x³+2x+2=f(x)

solve for x, f(x)=0 given first estimate is x₁=-1

formula is x₂=x₁-f(x₁)/f'(x₁)

f'(x)=3x²+2, at x=-1,,,f'(-1)=5

x₂= -4/5

use same formula again for x₃

I compute -794/1080

but you need to check