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Question 1: a) Show that the equation x^2-17x+13=0 can be arranged to give x= {\Large \frac{x^2+13}{17}} b) Starting with x_0=1 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+13}{17}} to obtain a solution of the equation x^2-17x+13=0 correct to 2 decimal places |

Question 2: a) Show that the equation x^2-29x+17=0 can be arranged to give x=- {\Large \frac{17}{x-29}} b) Starting with x_0=1 use the iterative formula x_{n+1} =- {\Large \frac{17}{x_n -29}} to obtain a solution of the equation x^2-29x+17=0 correct to 2 decimal places |

Question 3: a) Show that the equation x^2-31x+5=0 can be arranged to give x= \sqrt{31x-5} b) Starting with x_0=31 use the iterative formula x_{n+1} = \sqrt{31x_n -5} to obtain a solution of the equation x^2-31x+5=0 correct to 2 decimal places |

Question 4: a) Show that the equation x^2-23x+1=0 can be arranged to give x= {\Large \frac{x^2+1}{23}} b) Starting with x_0=0 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+1}{23}} to obtain a solution of the equation x^2-23x+1=0 correct to 2 decimal places |

Question 5: a) Show that the equation x^2-21x+11=0 can be arranged to give x=- {\Large \frac{11}{x-21}} b) Starting with x_0=1 use the iterative formula x_{n+1} =- {\Large \frac{11}{x_n -21}} to obtain a solution of the equation x^2-21x+11=0 correct to 2 decimal places |

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Question 1: a) x^2-17x+13=0 \implies x^2+13 =17x \implies x= {\Large \frac {x^2+13}{17}} b) Root to 2 decimal places = 0.80 |

Question 2: a) x^2-29x+17=0 \implies x^2-29x=-17 \implies x(x-29)=-17 \implies x=- {\Large \frac{17}{x-29}} b) Root to 2 decimal places = 0.60 |

Question 3: a) x^2-31x+5=0 \implies x^2 =31x -5 \implies x= \sqrt{31x-5} b) Root to 2 decimal places = 30.84 |

Question 4: a) x^2-23x+1=0 \implies x^2+1 =23x \implies x= {\Large \frac {x^2+1}{23}} b) Root to 2 decimal places = 0.04 |

Question 5: a) x^2-21x+11=0 \implies x^2-21x=-11 \implies x(x-21)=-11 \implies x=- {\Large \frac{11}{x-21}} b) Root to 2 decimal places = 0.54 |

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