Question

Find the positive root of x2 + 5x – 3 = 0 using fixed point

iteration starting with 0.6 as first approximation​

Answer 1

Given:

x² + 5x - 3 = 0

x₀ = 0.6

To find:

The positive root of x² + 5x – 3 = 0 using fixed point  iteration.

Solution:

Let f(x) = x² + 5x - 3

Here x² + 5x - 3 = 0

∴ x² + 5x - 3 = 0

∴ x(x + 5) = 3

∴ x = 3 / (x + 5)

∴ ∅(x) = 3 / (x + 5)

x₀ = 0.6

x₁ = ∅(x₀) = ∅(0.6)= 3 / (0.6 + 5) = 0.5357

x₂ = ∅(x₁) = ∅(0.5357) = 3 / (0.5357 + 5) = 0.5419

x₃ = ∅(x₂) = ∅(0.5419) = 3 / (0.5419 + 5) = 0.5413

x₄ = ∅(x₃) = ∅(0.5413) = 3 / (0.5413 + 5) = 0.5413

Approximate root of the equation x²+5x-3 using Iteration method is 0.5413 (After 4 iterations)