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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 = 72 . What value of x would you try next in the table below?
    x x^{2} + x comment
    6 42 Too low
    11 132 Too high
  2. Find the exact solution for x^{2} + x = 72
  3. 3x^{2} - x = 24 . What value of x would you try next in the table below?
    x 3x^{2} - x comment
    6 102 Too high
    2 10 Too low
  4. Find the exact solution for 3x^{2} - x = 24
  5. x^{3} - 3x = 52 . What value of x would you try next in the table below?
    x x^{3} - 3x comment
    1 -2 Too low
    7 322 Too high
  6. Find the exact solution for x^{3} - 3x = 52

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

  7. x^{2} - x = 45 (to 1 d.p.)
  8. x + x^{3} = 41 (to 1 d.p.)
  9. x\left( x - 4 \right) = 157 (to 2 d.p.)
  10. 2^{x} = 11 (to 2 d.p.)

    11. The product of two consecutive integers is 342

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