Question

Starting with x0 = 0 (x0 has diagonal 0 that is smaller and towards the bottom) use the iteration formuala xn+1 = 4/ xn^2 +5 twice (for xn+1 the n+1 is smaller than x and diagonal towards the bottom also for xn^2 the n^2 is smaller than the x and diagonal towards the bottom of it) find an estimate for the solution of x^3+5x-4=0


My work:
1:x=0 so 0 to the power of 0 plus one is 1. so 1 must equal 4/ xn^2+5.
2) xn^2 must also equal sero.
3)so 1= 4/0+5
4)so 1=4/5
5)so x is 4/5 so i put it in the x^3+5x-4=0.
6) 4/5^3+5*4/5-4=0

I am very very cnfused and unsure on this questions please help showing me step by step help and clear explanations. Please help me!

Answer 1

if x<0>=0 then 4/(x<0>)^2 is undefined. I'll assume that

x<n+1> = 4/(x<n>^2+5)

If so, then
x<0> = 0
x<1> = 4/(0^2+5) = 4/5 = 0.8
x<2> = 4/(0.8^2+5) = 4/5.64 = 0.7092
...

The actual root ≈ 0.72408

If I got the formula wrong, then adjust it, taking care with x<0>