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29 September, 21:40

X^3-5x=59 the soloution is between 4 and 5

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  1. 29 September, 23:29
    0
    True

    x = 4.32 (2 dp)

    Step-by-step explanation:

    x³ - 5x = 59

    x³ - 5x - 59 = 0

    x = 4

    4³ - 5 (4) - 59 = - 15

    x = 5

    5³ - 5 (5) - 59 = + 41

    A change in sign indicates the existence of root between 4 and 5

    Use iterative process to identify the root

    x³ - 5x - 59 = 0

    x³ = 5x + 59

    x = (5x + 59) ^⅓

    Start at any x between 4 and 5

    x (n+1) = (5x (n) + 59) ^⅓

    x0 = 4.8

    x1 = 4.362070671

    x2 = 4.323369309

    x3 = 4.319915667

    x4 = 4.319607202

    x5 = 4.318579649

    Clearly x is 4.32 (2 dp)
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