(i)[3]
Find the value of $\alpha$ correct to 3 decimal places. Show your working, and list each calculated sequence value to 5 decimal places.
(ii)[2]
Find, in the form $ax^3 + bx^2 + c = 0$, an equation for which $\alpha$ is a root.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The sequence $x_1, x_2, x_3, \ldots$ defined by $x_1 = 1$, $x_{n+1} = \frac{1}{2}\sqrt[3]{x_n^2 + 6}$ tends to the value $\alpha$.