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Question 1: a) Show that the equation x^2-13x+11=0 can be arranged to give x=- {\Large \frac{11}{x-13}} b) Starting with x_0=1 use the iterative formula x_{n+1} =- {\Large \frac{11}{x_n -13}} to obtain a solution of the equation x^2-13x+11=0 correct to 2 decimal places |

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

Question 3: a) Show that the equation x^2-21x+13=0 can be arranged to give x= {\Large \frac{x^2+13}{21}} b) Starting with x_0=1 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+13}{21}} to obtain a solution of the equation x^2-21x+13=0 correct to 2 decimal places |

Question 4: a) Show that the equation x^2-19x+3=0 can be arranged to give x=- {\Large \frac{3}{x-19}} b) Starting with x_0=0 use the iterative formula x_{n+1} =- {\Large \frac{3}{x_n -19}} 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^2-15x+19=0 can be arranged to give x= \sqrt{15x-19} b) Starting with x_0=14 use the iterative formula x_{n+1} = \sqrt{15x_n -19} to obtain a solution of the equation x^2-15x+19=0 correct to 2 decimal places |

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Question 1: a) x^2-13x+11=0 \implies x^2-13x=-11 \implies x(x-13)=-11 \implies x=- {\Large \frac{11}{x-13}} b) Root to 2 decimal places = 0.91 |

Question 2: a) x^2-17x+17=0 \implies x^2 =17x -17 \implies x= \sqrt{17x-17} b) Root to 2 decimal places = 15.93 |

Question 3: a) x^2-21x+13=0 \implies x^2+13 =21x \implies x= {\Large \frac {x^2+13}{21}} b) Root to 2 decimal places = 0.64 |

Question 4: a) x^2-19x+3=0 \implies x^2-19x=-3 \implies x(x-19)=-3 \implies x=- {\Large \frac{3}{x-19}} b) Root to 2 decimal places = 0.16 |

Question 5: a) x^2-15x+19=0 \implies x^2 =15x -19 \implies x= \sqrt{15x-19} b) Root to 2 decimal places = 13.60 |

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