Transcript Trial and Improvement

Trial and Improvement
Finding a solution
Use trial and Improvement to solve
x³ = 54 to one decimal place
x
x³
3
3³ = 27
Too small
4
3.5
4³ = 64
(3.5)³=42.875
Too big
Too small
3.8
(3.8)³=54.872
Too big
3.7
(3.7)³=50.653
Too small
3.75
(3.75)³=52.734
Too small
Solution
 Take x=3.8 as it is closest.
 When you round 3.75 to one decimal
place it becomes 3.8.
Example 2
 A solution for the
equation x³+2x=40
lies between 3 and 4.
Find this solution to
one decimal place.
x³+2x=40
X
x³+2x
3
3³+2x3=33
Too small
4
4³+2x4=72
Too big
3.5
Too big
3.2
3.5³+2x3.5=
49.875
39.168
3.3
42.537
Too big
3.25
40.828125
Too big
Too small
Solution x³+2x=40
 Take the solution x =3.2 as it is the
closest.
 X=3.25 was too big and as this rounds to
3.3 the solution is therefore x=3.2