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Question 1: a) Show that the equation x^2-25x+3=0 can be arranged to give x= {\Large \frac{x^2+3}{25}} b) Starting with x_0=0 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+3}{25}} to obtain a solution of the equation x^2-25x+3=0 correct to 2 decimal places |

Question 2: a) Show that the equation x^2-11x+15=0 can be arranged to give x=- {\Large \frac{15}{x-11}} b) Starting with x_0=2 use the iterative formula x_{n+1} =- {\Large \frac{15}{x_n -11}} to obtain a solution of the equation x^2-11x+15=0 correct to 2 decimal places |

Question 3: a) Show that the equation x^2-31x+17=0 can be arranged to give x= \sqrt{31x-17} b) Starting with x_0=30 use the iterative formula x_{n+1} = \sqrt{31x_n -17} to obtain a solution of the equation x^2-31x+17=0 correct to 2 decimal places |

Question 4: a) Show that the equation x^2-19x+11=0 can be arranged to give x= {\Large \frac{x^2+11}{19}} b) Starting with x_0=1 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+11}{19}} to obtain a solution of the equation x^2-19x+11=0 correct to 2 decimal places |

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

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Question 1: a) x^2-25x+3=0 \implies x^2+3 =25x \implies x= {\Large \frac {x^2+3}{25}} b) Root to 2 decimal places = 0.12 |

Question 2: a) x^2-11x+15=0 \implies x^2-11x=-15 \implies x(x-11)=-15 \implies x=- {\Large \frac{15}{x-11}} b) Root to 2 decimal places = 1.59 |

Question 3: a) x^2-31x+17=0 \implies x^2 =31x -17 \implies x= \sqrt{31x-17} b) Root to 2 decimal places = 30.44 |

Question 4: a) x^2-19x+11=0 \implies x^2+11 =19x \implies x= {\Large \frac {x^2+11}{19}} b) Root to 2 decimal places = 0.60 |

Question 5: a) x^2-13x+5=0 \implies x^2-13x=-5 \implies x(x-13)=-5 \implies x=- {\Large \frac{5}{x-13}} b) Root to 2 decimal places = 0.40 |

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