The sequence of values given by the iterative formula $$$x_{n+1}=\frac{6+8 x_{n}}{8+x_{n}^{2}}$$$ with initial value $$$x_{1}=2$$$ converges to $$$\alpha$$$. State an equation satisfied by $$$\alpha$$$ and hence determine the exact value of $$$\alpha$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_21 Year：2020 Question No：5(b)

Answer:

State equation $x=\frac{6+8 x}{8+x^{2}}$ or equivalent using $\alpha$
Obtain $\sqrt[3]{6}$ or exact equivalent

2.6.2 understand the idea of, and use the notation for, a sequence of approximations which converges to a root of an equation