Math Problem Statement
The iterative formula below will give an approximate solution to the equation x^3 + 2x^2 − 3x = 12. Use this formula to work out an approximate solution to the equation starting with x₁ = 0, and calculate the difference between the rounded solution and the actual value when substituted back into the equation.
Solution
Let's break this problem into two parts, as outlined in the question.
Part (a)
We are given the iterative formula: and need to compute the approximate solution starting with , giving the answer to 3 decimal places.
- Starting with :
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Math Problem Analysis
Mathematical Concepts
Iterative Methods
Algebraic Equations
Roots of Equations
Formulas
x_{n+1} = sqrt((3x_n + 12) / (x_n + 2))
f(x) = x^3 + 2x^2 − 3x
Theorems
Fixed Point Iteration
Suitable Grade Level
Grades 10-12
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