Answer:
The solution to the equation x³ - 3x = 1 is given as :
1.88
Step-by-step explanation:
In the above question, we are given the equation
x³ - 3x = 1 ... Equation 1
and we are told the answer lies between 1.8 - 1.9
Using the trial and improvement method approximating to 2 decimal places
a. First trial we use 1.84 for x in equation 1
1.84³ - 3×1.84 = 0.71
This first trial using 1.84 too small
b. Second trial we use 1.86 for x in equation 1
1.86³ - 3×1.86 = 0.86
This second trial using 1.86 as well is too small
c. For our third trial we use 1.89 for x in equation 1
1.89³ - 3×1.89 = 1.08
This third trial using 1.89 is large. Our target is 1.00
d. Our fourth trial we use 1.88 for x in equation 1
1.88³ - 3×1.88 = 1.004
Approximately to 2 decimal places.
We have = 1.00
Hence the solution to the equation
x³ - 3x = 1 after using the trial and improvement method is 1.88
