## Exam-Style Question on Iteration## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 199. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

Consider the following cubic equation:

$$x^3-7x-5=0$$

An approximate solution can be found by using the following iterative process.

$$x_{n+1}=\frac{(x_n)^3-5}{7}$$(a) Find \(x_2\) and \(x_3\) if \(x_1=-1\)

Work out the solution to 6 decimal places.

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