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trial and improvement

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The equation
X*X*X-X=45
has a solution between 3 and 4
use a trial and improvement method to find this solution
give your solution correct to 1 decimal place
you must show all you working
Guest Mar 1, 2012
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tom:

The equation
X*X*X-X=45
has a solution between 3 and 4
use a trial and improvement method to find this solution
give your solution correct to 1 decimal place
you must show all you working

step 1:
X=3
X*X*X-X = X^3-3 = 3^3-3 = 24

step2:
X=4
X*X*X-X = X^3-4 = 4^3-4 = 60

step3: (left=3, right=4)
middle = (left+right)/2 = (3+4)/2 = 7/2 = 3.5
X*X*X-X = 3.5^3-3.5 = 39.375
here you see, that the right side of the equation 45 is between 39.375 and 60. so the X is between middle and right (3.5 and 4) and not between (3 and 3.5).

step4: (left=3.5, right=4)
middle = (left+right)/2 = (3.5+4)/2 = 3.75
X*X*X-X = 3.75^3-3.75 = 48.984375
so X is between left and middle.

step5: (left=3.5, right=3.75)
and so on...

[input]X*X*X-X=45[/input]