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

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)