We want to find one of the roots of a cubic equation given by 1 0 3 x + x − = which is between 0 and 1 by an iterative method. Modify the equation above to 2 1 1 x x + = Start with an appropriate initial value and do the iteration above until it is convergent. For example, 0.8, 1 0.5 1 0.5 , 0 1 2 = + x = x = 0.609, 1 0.8 1 2 2 = + x = 0.728,  1 0.609 1 3 2 = + x = The simplest (minimum) code may look like:

Respuesta :

Answer:

0.682

Step-by-step explanation:

[tex]x = \frac{1}{1 + x^2}[/tex]

continuing the iteration from x₃ giving in the question

x₃ = 0.728

x₄ = 0.653

x₅ = 0.701

x₆ = 0.671

x₇ = 0.690

x₈ = 0.678

x₉ = 0.685

x₁₀ = 0.680

x₁₁ = 0.683

x₁₂ = 0.681

x₁₃ = 0.682

x₁₄ = 0.681

x₁₅ = 0.682

x₁₆ = 0.682

x₁₇ = 0.682

The equation converges to 0.682

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