Final answer:
The iterative process is used to approximate the solution to an equation. The values of x₂ and x₃ are found using the given formula. To find the solution to 6 decimal places, we continue the iterative process.
Step-by-step explanation:
In this problem, we are given an iterative process to approximate the solution to an equation. We start with x₁ = -1 and use the given formula to find x₂ and x₃.
(i) To find x₂, we substitute x₁ = -1 into the formula: x₂ = (-1)³ - 5/10 = -1 - 0.5 = -1.5.
(ii) To find x₃, we substitute x₂ = -1.5 into the formula: x₃ = (-1.5)³ - 5/10 = -3.375.
(b) To find the solution to 6 decimal places, we can continue the iterative process using the given formula until we reach the desired accuracy. Based on the given answer, the approximate solution to 6 decimal places is -0.5216.