The equation x^3-5x=59 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answer to one dec

Question

The equation x^3-5x=59 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answer to one decimal place. You must show all your working. On the same line as your final answer, you must write to “1 decimal place”.

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Ngọc Hoa 5 years 2021-07-18T17:40:39+00:00 1 Answers 199 views 0

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  1. vankhanh
    0
    2021-07-18T17:42:15+00:00
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    Answer:

    The answer is “4.3“.

    Step-by-step explanation:

    Given:

    \to x^3 - 5x - 59 = 0

    When x = 4.1:  

    \to f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579

    When x= 4.2:

    f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912

    When x = 4.3:

    \to f(4.3) = -0.993 (closer to 0)

    \to f(4.4) = 4.184

    • It changes the sign so, the root lies in 4.3 and 4.4.

    When x = 4.35:

    \to f(4.35) = 1.563

    When the root is closer to 4.3 than 4.4 So, 1.563 is closer to zero than 4.184.

    When x = 4.32:

    \to f(4.32) = 0.0216 close to zero.

    So the answer is 4.3 to 1 decimal place.  

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