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QMMaths

Trial and Improvement

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Answers

    For each equation below, write the next value of x that you would try in the table and find the solution to the equation

  1. x^{2} + x = 42 . What value of x would you try next in the table below?
    x x^{2} + x comment
    3 12 Too low
    9 90 Too high
  2. Find the exact solution for x^{2} + x = 42
  3. 3x^{2} - x = 70 . What value of x would you try next in the table below?
    x 3x^{2} - x comment
    4 44 Too low
    8 184 Too high
  4. Find the exact solution for 3x^{2} - x = 70
  5. x^{3} - 2x = 115 . What value of x would you try next in the table below?
    x x^{3} - 2x comment
    6 204 Too high
    3 21 Too low
  6. Find the exact solution for x^{3} - 2x = 115

    7. Using trial and improvement, find the solution to the following equations to the given number of decimal places

  7. x^{2} - x = 63 (to 1 d.p.)
  8. x + x^{3} = 25 (to 1 d.p.)
  9. x\left( x - 2 \right) = 34 (to 2 d.p.)
  10. 2^{x} = 9 (to 2 d.p.)

    11. The product of two consecutive integers is 182

  11. Calling x the smallest of the two integers, write an equation for x.
  12. Using trial and improvement, find the value of x