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Question 1: a) Show that the equation x^2-13x+19=0 can be arranged to give x= \sqrt{13x-19} b) Starting with x_0=11 use the iterative formula x_{n+1} = \sqrt{13x_n -19} to obtain a solution of the equation x^2-13x+19=0 correct to 2 decimal places |

Question 2: a) Show that the equation x^2-27x+1=0 can be arranged to give x= {\Large \frac{x^2+1}{27}} b) Starting with x_0=0 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+1}{27}} to obtain a solution of the equation x^2-27x+1=0 correct to 2 decimal places |

Question 3: 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 |

Question 4: a) Show that the equation x^2-29x+15=0 can be arranged to give x= \sqrt{29x-15} b) Starting with x_0=28 use the iterative formula x_{n+1} = \sqrt{29x_n -15} to obtain a solution of the equation x^2-29x+15=0 correct to 2 decimal places |

Question 5: a) Show that the equation x^2-11x+17=0 can be arranged to give x= {\Large \frac{x^2+17}{11}} b) Starting with x_0=2 use the iterative formula x_{n+1} = {\Large \frac{x_n^2+17}{11}} to obtain a solution of the equation x^2-11x+17=0 correct to 2 decimal places |

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Question 1: a) x^2-13x+19=0 \implies x^2 =13x -19 \implies x= \sqrt{13x-19} b) Root to 2 decimal places = 11.32 |

Question 2: a) x^2-27x+1=0 \implies x^2+1 =27x \implies x= {\Large \frac {x^2+1}{27}} b) Root to 2 decimal places = 0.04 |

Question 3: 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 |

Question 4: a) x^2-29x+15=0 \implies x^2 =29x -15 \implies x= \sqrt{29x-15} b) Root to 2 decimal places = 28.47 |

Question 5: a) x^2-11x+17=0 \implies x^2+17 =11x \implies x= {\Large \frac {x^2+17}{11}} b) Root to 2 decimal places = 1.86 |

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