Question

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

Answer 1

Explanation:

x = 4.32 (2 dp)

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)

Answer 2

True

x = 4.32 (2 dp)

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)