Question

Please help and add an explanation if you can <3

Answer 1

The value of
`x_2 = 1`

Solution:

Given that a approximate solution to the equation
`x^2 +6x - 2=0` can be calculated using the iterative formula shown below

`x_(n+1) = (2-(x_n)^3)/(6)`

Also given that
`x_1 =2`

To find: value of
`x_2`

To find value of
`x_2` , substitute n = 1 in given iterative formula

`x_(1+1) = (2-(x_1)^3)/(6)`

Solve the above expression by substituting
`x_1 = 2`

`x_2 = (2-(2)^3)/(6)`

`x_2 = (2-8)/(6)\\\\x_2 = (-6)/(6)\\\\x_2 = -1`

Thus value of
`x_2 = 1`