- 8. Solving Equations using Trial and Improvement
1.
The number x satisfies the equation x3 = 20.
(a)
Between which two consecutive whole numbers does x lie?
..................................................................................................................................
(1)
(b)
Use a trial and improvement method to find this value of x correct to one
decimal place. Show all your working clearly.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(3)
2.
Use trial and improvement to find a solution, to 1 decimal place, of the equation.
x³ + x = 100. Show all your trials in the table. A first trial has been done for you.
x
x3 + x
Comment
5
130
Too big
(4)
3.
Use trial and improvement to find a solution to the equation x3– 5x = 56.
This table shows the first two trials.
x
x3 – 5x
Comment
4
44
Too small
5
100
Too big
Continue the table to find a solution to the equation.
Give your answer to 1 decimal place.
(3)
Hamilton Community College