Final answer:
The value of x₂ using the iterative process Xₙ₊₋ = (Xₙ)³ - 1 / 4 with x₁ = -1 is -0.5.
Step-by-step explanation:
The question involves an iterative process to find an approximate solution to an equation. Given the formula X₍ₙ₊₋₍₍₁ = (X₍ₙ)³ - 1 / 4 with an initial value of x₍₁ = -1, we need to calculate the value of x₍₂.
To find x₍₂, we substitute x₍₁ into the iterative formula:
x₍₂ = ((-1)³ - 1) / 4
x₍₂ = (-1 - 1) / 4
x₍₂ = -2 / 4
x₍₂ = -0.5
Using the iterative process formula, the calculated value of x₍₂, which is the second iteration starting from x₍₁ = -1, is -0.5.