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Kemp
Mathematics
28 February, 10:13
X^3-5x=59 the soloution is between 4 and 5
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28 February, 10:29
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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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