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

$x_{n+1} = \frac{2-(x_n)^3}{6}$

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

$x_{1+1} = \frac{2-(x_1)^3}{6}$

Solve the above expression by substituting $x_1 = 2$

$x_2 = \frac{2-(2)^3}{6}$

$x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1$

Thus value of $x_2 = 1$