The value of [tex]x_2 = 1[/tex]
Solution:
Given that a approximate solution to the equation [tex]x^2 +6x - 2=0[/tex] can be calculated using the iterative formula shown below
[tex]x_{n+1} = \frac{2-(x_n)^3}{6}[/tex]
Also given that [tex]x_1 =2[/tex]
To find: value of [tex]x_2[/tex]
To find value of [tex]x_2[/tex] , substitute n = 1 in given iterative formula
[tex]x_{1+1} = \frac{2-(x_1)^3}{6}[/tex]
Solve the above expression by substituting [tex]x_1 = 2[/tex]
[tex]x_2 = \frac{2-(2)^3}{6}[/tex]
[tex]x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1[/tex]
Thus value of [tex]x_2 = 1[/tex]
