1.
$$f ( x ) = 2 x ^ { 3 } + x - 20$$
- Show that the equation \(\mathrm { f } ( x ) = 0\) can be rewritten as
$$x = \sqrt [ 3 ] { a - b x }$$
where \(a\) and \(b\) are positive constants to be determined.
- Starting with \(x _ { 1 } = 2.1\) use the iteration formula \(x _ { n + 1 } = \sqrt [ 3 ] { a - b x _ { n } }\), with the numerical values of \(a\) and \(b\), to calculate the values of \(x _ { 2 }\) and \(x _ { 3 }\) giving your answers to 3 decimal places.
- Using a suitable interval, show that 2.077 is a root of the equation \(\mathrm { f } ( x ) = 0\) correct to 3 decimal places.
- Hence state a root, to 3 decimal places, of the equation
$$2 ( x + 2 ) ^ { 3 } + x - 18 = 0$$
| VIIIV SIHI NI JIIYM ION OC | VIIV SIHI NI JIIIM ION OC | VIIV SIHI NI JIIYM ION OC |