Question

Use the iterative formula, x = √5x, -8 to calculate a solution to 3 dp

of x³-5x+8=0. Start with x₁ = -3.

Answer 1

x ≈ -2.803

Explanation:

You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.

Iteration

Your iterator appears to be found by solving for x:

x³ -5x +8 = 0

x³ = 5x -8 . . . . . . add 5x-8

x = ∛(5x -8) . . . . take the cube root

The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.

__

Additional comment

Using a faster-converging iteration technique, we find the solution to be about ...

x ≈ -2.8025​887521

The solution above is accurate to 3 dp.