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Question 1: a) Show that the equation x^2-17x+11=0 can be arranged to give x= \sqrt{17x-11} b) Starting with x_0=16 use the iterative formula x_{n+1} = \sqrt{17x_n -11} to obtain a solution of the equation x^2-17x+11=0 correct to 2 decimal places |

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

Question 3: a) Show that the equation x^2-9x+9=0 can be arranged to give x=- {\Large \frac{9}{x-9}} b) Starting with x_0=1 use the iterative formula x_{n+1} =- {\Large \frac{9}{x_n -9}} to obtain a solution of the equation x^2-9x+9=0 correct to 2 decimal places |

Question 4: a) Show that the equation x^2-19x+3=0 can be arranged to give x= \sqrt{19x-3} b) Starting with x_0=19 use the iterative formula x_{n+1} = \sqrt{19x_n -3} to obtain a solution of the equation x^2-19x+3=0 correct to 2 decimal places |

Question 5: a) Show that the equation x^2-13x+1=0 can be arranged to give x= {\Large \frac{x^2+1}{13}} b) Starting with x_0=0 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+1}{13}} to obtain a solution of the equation x^2-13x+1=0 correct to 2 decimal places |

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Question 1: a) x^2-17x+11=0 \implies x^2 =17x -11 \implies x= \sqrt{17x-11} b) Root to 2 decimal places = 16.33 |

Question 2: a) x^2-21x+5=0 \implies x^2+5 =21x \implies x= {\Large \frac {x^2+5}{21}} b) Root to 2 decimal places = 0.24 |

Question 3: a) x^2-9x+9=0 \implies x^2-9x=-9 \implies x(x-9)=-9 \implies x=- {\Large \frac{9}{x-9}} b) Root to 2 decimal places = 1.15 |

Question 4: a) x^2-19x+3=0 \implies x^2 =19x -3 \implies x= \sqrt{19x-3} b) Root to 2 decimal places = 18.84 |

Question 5: a) x^2-13x+1=0 \implies x^2+1 =13x \implies x= {\Large \frac {x^2+1}{13}} b) Root to 2 decimal places = 0.08 |

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