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27 April, 19:23

the equation x^3-3x=1 has a solution between 1.8 and 1.9. use a trial and improvement method to find this solution. give your answer correct to 2 decimal places.

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  1. 27 April, 22:48
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    The solution to the equation x³ - 3x = 1 is given as:

    1.88

    Step-by-step explanation:

    In the above question, we are given the equation

    x³ - 3x = 1 ... Equation 1

    and we are told the answer lies between 1.8 - 1.9

    Using the trial and improvement method approximating to 2 decimal places

    a. First trial we use 1.84 for x in equation 1

    1.84³ - 3*1.84 = 0.71

    This first trial using 1.84 too small

    b. Second trial we use 1.86 for x in equation 1

    1.86³ - 3*1.86 = 0.86

    This second trial using 1.86 as well is too small

    c. For our third trial we use 1.89 for x in equation 1

    1.89³ - 3*1.89 = 1.08

    This third trial using 1.89 is large. Our target is 1.00

    d. Our fourth trial we use 1.88 for x in equation 1

    1.88³ - 3*1.88 = 1.004

    Approximately to 2 decimal places.

    We have = 1.00

    Hence the solution to the equation

    x³ - 3x = 1 after using the trial and improvement method is 1.88
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